Bài tập CALCULUS 26

Created by T Madas Question 99 (***+) y = − x2 + 8x − y y = x − 10 x + 26 A B R O x The figure above shows the graphs of the curves with equations y = − x + x − and y = x − 10 x + 26 The two curves intersect each other at the points A and B The finite region R bounded by the two curves is shown shaded in the figure above Show that the area of R is exactly 125 C2L , proof Created by T Madas Created by T Madas Question 100 (***+) 25x 15x y 20x The figure above shows a solid triangular prism with a total surface area of 3600 cm The triangular faces of the prism are right angled with a base of 20x cm and a height of 15x cm The length of the prism is y cm a) Show that the volume of the prism, V cm3 , is given by V = 9000 x − 750 x3 b) Find the value of x for which V is stationary c) Show that the value of x found in part (b) gives the maximum value for V d) Determine the value of y when V is maximum C2D , x = , y = 20 Created by T Madas Created by T Madas Question 101 (***+) The curve C has equation y = ax − b x2 , x ≠ 0, where a and b are non zero constants The gradient of C at the points where x = and x = −2 is 14 and , respectively Find the value of a and the value of b a = 6, b = Question 102 (***+) f ′( x) = − x2 , x ≠ Find the value of f ( ) , given that f (1) = + f ( ) C1X , f ( ) = 14 Created by T Madas