Bài tập CALCULUS 23

Created by T Madas Question 88 (***+) r h The figure above shows a closed cylindrical can of radius r cm and height h cm a) Given that the surface area of the can is 192π cm , show that the volume of the can, V cm3 , is given by V = 96π r − π r b) Find the value of r for which V is stationary c) Justify that the value of r found in part (b) gives the maximum value for V d) Calculate the maximum value of V MP1-K , r = ≈ 5.66 , Vmax = 256π ≈ 1137 Created by T Madas Created by T Madas Question 89 (***+) The curve C has equation y = x3 − x + 12 x − 10 a) Find the coordinates of the two points on the curve where the gradient is zero The point P lies on C and its x coordinate is −1 b) Determine the gradient of C at the point P The point Q lies on C so the gradient at Q is the same as the gradient at P c) Find the coordinates of Q C1G , (1, −5 ) , ( 2, −6 ) , 36 , Q ( 4, 22 ) Created by T Madas Created by T Madas Question 90 (***+) The gradient function at every point on a curve C is given by dy = ( kx − 3) x , dx where k is a non zero constant The point P ( 4, 40 ) lies on C and the gradient at P is 34 Determine an equation of C C1V , y = x − x − Created by T Madas