Bài tập CALCULUS 21

Created by T Madas Question 82 (***) The curve C with equation y = f ( x ) satisfies f ′( x) = − x2 , x ≠ a) Given that f (1) = , find an expression for f ( x ) b) Sketch the graph of f ( x ) , indicating clearly the asymptotes of the curve and the coordinates of any points where the curve crosses the coordinate axes C1D , f ( x ) = Created by T Madas −2 , x ( 2,0 ) Created by T Madas Question 83 (***) The total cost C , in £ , for a certain car journey, is modelled by C= 200 2V + , V > 30 , V 25 where V is the average speed in miles per hour a) Find the value of V for which C is stationary b) Justify that this value of V minimizes C c) Hence determine the minimum total cost of the journey C2J , V = 50 , £8 Created by T Madas Created by T Madas Question 84 (***) x A y B G F 1c E x y C D The figure above shows a clothes design consisting of two identical rectangles attached to each of the straight sides of a circular sector of radius x cm The rectangles measure x cm by y cm and the circular sector subtends an angle of one radian at the centre The perimeter of the design is 40 cm a) Show that the area of the design, A cm , is given by A = 20 x − x b) Determine by differentiation the value of x for which A is stationary c) Show that the value of x found in part (b) gives the maximum value for A d) Find the maximum area of the design SYN-H , x = 10 , Amax = 100 Created by T Madas