Bài tập Toán INTEGRATION 12

Created by T Madas Question 33 y y = f ( x) O P ( −1,0 ) Q x The figure above shows a curve with equation y = f ( x ) The curve meets the x axis at the points P ( −1,0 ) and Q , and its gradient function is given by f ′( x) = x3 − x2 , x ≠ a) Find an equation of the tangent to the curve at P b) Find an expression for f ′′ ( x ) c) Determine … i … an equation of the curve ii … the coordinates of Q y = −9 x − , f ′′ ( x ) = + x −3 , y = x + Created by T Madas − , Q ,0 x ( ) Created by T Madas Question 34 +5 x , x > x y= Show clearly that ∫ y dx = 1931 proof Created by T Madas Created by T Madas Question 35 A quadratic curve C passes through the points P ( a, b ) and Q ( 2a, 2b ) , where a and b are constants The gradient at any given point on C is given by dy = 2x − dx Find an equation for C , in terms of a y = x − x + 2a Created by T Madas