Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống
1
/ 18 trang
THÔNG TIN TÀI LIỆU
Nội dung
Project 02: The Second Derivative Test Kiểm tra đạo hàm cấp Lớp: DT01 – N02 GVHD: TS Nguyễn Đình Dương ĐẠI HỌC QUỐC GIA THÀNH PHỐ HỒ CHÍ MINH TRƯỜNG ĐẠI HỌC BÁCH KHOA PHÂN CÔNG NHIỆM VỤ MSSV Họ và tên Nhiệm vụ Mức độ hoàn thành 2012629 Trần Sơn Ánh Thực Task 1,3,5,7 + Tổng hợp, chỉnh sửa 100% 2011367 Nguyễn Phúc Khang Thực Task 2,4,6,8 + Ví dụ mở rộng 100% 1812846 Dương Hồng Long Soạn thảo PowerPoint + BÁO CÁO 100% 1813209 Phan Thị Kim Ngân Chuẩn bị lý thuyết liên quan đến đề tài + Soạn thảo Word 100% 1915831 Nguyễn Minh Tùng Soạn thảo Word + Tổng hợp 100% NATIONAL UNIVERSITY OF HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 CƠ SỞ LÝ THUYẾT THỰC HÀNH MỞ RỘNG NHẬN XÉT Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 CƠ SỞ LÝ THUYẾT Mục tiêu: Một hạn chế phép thử Đạo hàm thứ hai cho hàm biến thực (vì giá trị tới hạn ) phép thử đạo hàm thứ hai không cung cấp thông tin việc liệu có phải cực đại cực tiểu hay khơng Trong dự án này, nhóm minh họa cách nhận thêm thông tin cách sử dụng khái niệm liên quan đến dòng Maclaurin Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Phân tích dựa chuỗi Maclaurin thực tế nếu: , số nguyên số dương với giá trị , cực tiểu hàm số , số nguyên số âm với giá trị , cực đại hàm số , số nguyên, đồ thị dương với số giá trị gần âm với số giá trị khác gần , khơng phải cực tiểu cực đại hàm số Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Khai triển chuỗi Maclaurin cho hàm có giá trị thực là: Nếu điểm tới hạn , thì: Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Nếu ta biết , thì: Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Trong số nguyên dương mà Khi số theo sau gần tiến dần 0: Do ta phân loại tính chất cách phân loại tính chất Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 THỰC HÀNH Ta có: Khi gần Mà đạt cực đại Hàm số đạt cực đại Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Ta có: Khi gần Mà khơng có cực đại cực tiểu Hàm số khơng có cực đại cự tiểu 10 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Ta có: Khai triển Maclaurin Khi gần là: Mà đạt cực tiểu Hàm số đạt cực tiểu 11 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 12 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Ta có: Khai triển Maclaurin là: ÞKhai triển Maclaurin là: Nên khai triển Maclaurin là: 13 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Khi gần Mà khơng có cực đại cực tiểu Hàm số khơng có cực đại cực tiểu 14 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 VÍ DỤ MỞ RỘNG Khai triển Maclaurin hàm số f ( x) ln(cos x); x ; đến số hạng x6 2 ln(cos x) ln sin x ln 1 sin x Khi x = sin2x = nên ta áp dụng cơng thức ln(1+x) u2 u3 u4 u5 u6 Khi đó: ln(1 u ) u 15 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Do ta có: sin x sin x sin x ln sin x sin x 2 (do bậc thấp sinx x nên u4 = sin8x có bậc vượt 6), mà: x3 x5 x6 x x6 sin x x x x x6 120 36 120 x x6 x2 x6 45 x3 x3 x6 sin x x x6 x4 x6 x x 4x Sin6x = x6 + 0(x6) Nên ta có: ln(cos x) x2 x4 x6 ln sin x x6 2 12 45 16 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 NHẬN XÉT Việc xác định điểm cực trị dễ dàng sử dụng khai triển Maclaurin trường hợp x = khiến đạo hàm cấp cấp hàm số f Điều áp dụng trường hợp x ≠ dẫn đến đạo hàm cấp cấp hàm số f Ta cần thay đổi khai triển Maclaurin thành khai triển Taylor x ý đến giá trị x xung quanh điểm Nếu ta biết đạo hàm cấp cấp hàm số f x = khơng biết cách khai triển Maclaurin ta bỏ qua bước tiếp tục tìm đạo hàm bậc cao hàm số f Cho đến ta thu đạo hàm cấp N hàm số f khác 0, tùy thuộc vào N chẵn hay lẻ N chẵn ta dựa vào hàm số để đưa kết luận điểm cực đại hay điểm cực tiểu 17 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2 Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2Project.02.The.Second.Derivative.Test.Kiem.tra.dao.ham.cap.2