Page 80 - Past Year

78 | P a g e

CHAPTER 9: APPLICATION OF DIFFERENTIATION

1. A furniture company produces units of table daily. The demand function and average

cost function (in RM) are given   400 2p q   q and   q  2q   400 respectively.
4
C
q
Find the

(a) revenue function, ( )
(b) cost function, ( ), and

(c) maximum profit of the company

2
3
f
2. Given that   x   x  9x  15x  11. Find the maximum and minimum points,

3. Given that the demand function is p   300 4x   x and the cost function is

2
C   x  x  150x  5000 where is the number of products. Determine
(a) the revenue function, ( ) and the profit function   x ,

(b) the maximum profit,

(c) the selling price to get the maximum profit,

2
5
4. Given y  x  7x  . Find the equation of normal to the curve at the point (1,3).

5. A company produces and sells pots each year with cost function,


2
x
p
C   4000 4x   x  0.005x and demand function,   160 0.2x , where x is the
number of pots, ( ) and ( ) are in RM. Find:
(a) the revenue function and the number of pots that should be sold to maximize the
revenue,

(b) the profit function and the maximum profit,
(c) the selling price to ensure maximum profit.

2
3

6. Find the equation of tangents to the curve x  3xy y  at point = 2.
8