ĐỀ THI, BÀ TẬP, TÀI LIỆU THAM KHẢO,
Created by T Madas Question 47 (***) h x 2x The figure above shows the design of a fruit juice carton with capacity of 1000 cm3 The design of the carton is that of a closed cuboid whose base measures x cm by x cm , and its height is h cm a) Show that the surface area of the carton, A cm , is given by A = x2 + 3000 x b) Find the value of x for which A is stationary c) Calculate the minimum value for A , justifying fully the fact that it is indeed the minimum value of A MP1-P , x = 375 ≈ 7.21 , Amin ≈ 624 Created by T Madas Created by T Madas Question 48 (***) The point P , where x = , lies on the curve C whose equation is y = x3 − x + x + a) Find an equation of the tangent to C at the point P b) Show that there is no other point on C where the gradient is the same as the gradient at P y = 11 − x Question 49 (***) x6 +1 y= , x >0 x Show clearly that a y dx = ax a + a x +C , where a is a rational constant to be found, and C is an arbitrary constant a = or 3 Created by T Madas Created by T Madas Question 50 (***) The cubic equation C passes through the origin O and its gradient function is dy = x − x − 20 dx a) Show clearly that the equation of C can be written as y = x ( x + a )( x + b ) , where a and b are constants b) Sketch the graph of C , indicating clearly the coordinates of the points where the graph meets the coordinate axes C1G , a = , b = −4 Created by T Madas