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31. Find the equation of the normal line for the curve y   x  3x  at = 1.

x 3 x 2 4
32. Determine the maximum point and the minimum point of the curve y    2x 
3 2 3

by using the second derivative test.

33. The total revenue function and total cost function of a company that produced one model


2

of handphone are   2000R x  x x and   4000 200x respectively where x is the

C
x
number of units of handphone produced. Find
(a) the marginal cost function and the profit function
(b) the number of handphone to be produced to maximize the profit
(c) the price of handphone per unit when the profit was maximized

x  4
2
f
34. Given   x 
8
x 3
  2 x  2 16 
' f
(a) Show that   x  11 by using quotient rule. Hence find all the stationary
3x 3
points.

(b) Using the second derivatives test, determine the relative minimum and maximum
for the curve ( ) at all stationary points.

35. The management of a company estimates that the cost (in RM) to produce x units of a
2
certain products is given by   0.015C x  x  10x  300. The revenue generated after

2
selling x units of this products is   60R x  x  0.01 . Find
x
(a) the maximum profit

(b) the selling price per unit in order to maximize the profit
(c) the level of production so that the average cost is minimum.

3
2
36. Find the equation of normal to the curve y  2x  4x   at point (2, −4).
x
6