Bài tập CALCULUS 15

Created by T Madas Question 60 (***) y y = x ( x − 1)( x − 3) O x A B The figure above shows part of the curve with equation y = x ( x − 1)( x − 3) , x ∈ » The curve meets the x axis at the origin and at the points A and B Determine the exact area of the finite region bounded by the curve and the x axis, shown shaded in the figure above C2B , area = 37 Created by T Madas Created by T Madas Question 61 (***) h x 4x The figure above shows a box in the shape of a cuboid with a rectangular base x cm by 4x cm and no top The height of the box is h cm It is given that the surface area of the box is 1728 cm2 a) Show clearly that 864 − x h= 5x b) Use part (a) to show that the volume of the box , V cm3 , is given by ( ) V = 432 x − x3 c) Find the value of x for which V is stationary d) Find the maximum value for V , justifying the fact that it is the maximum x = 12 , Vmax = 5529.6 Created by T Madas Created by T Madas Question 62 (***) The curve C and the line L have equations C : y = 16 x + 32 − 35 and L : y + x = 14 x Show that L is a normal to C at the point where x = proof Question 63 (***) The curve C has equation y = ax − x + , x >0, x where a is a non zero constant Given that dy = at the point on C where x = , find the value of a dx C1H , a = 16 Created by T Madas