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(b) Calculate the daily production that maximizes the profit and what is the maximum

profit.

13. The equation of the tangent to the curve x y ay 2 2  b at the point (1,2) is 4x  3y  7

where and are constants. Find the values of and .

C
14. The demand function p(x) and the average cost function   x for Syarikat ABC are given
as   240 20p x   x and   5C x  x  40 . Find

(a) the cost function, the revenue function, and the profit function

(b) determine the quantity and the price needed to maximize the total revenue
(c) The profit and total revenue that will give maximum profit.

dy
2
2
15. Given that the curve 2x  4xy  4y  8,find the expression for in term of and .
dx
Hence, find the points in the curve where the tangent is parallel to -axis.


16. The demand function for a product is x  3000 25p where is the number of unit
demanded and is the price in RM.

(a) Determine the price that should be charged to maximize the total revenue.

(b) Find the maximum revenue.


2
17. Find the equation of the normal line to the curve y  x xy  3 at the coordinate (1,1).

3
18. Given a curve y  12x  2 2x .
(a) Determine the two stationary points of the above curve. Hence, determine whether
the two stationary points are maximum or minimum points.

(b) The gradient at a point of the above curve is 24. Find the equation of the tangent
line at the point .

2
4
19. Find the equation of the normal line to the curve 2y  xy  2x  at the coordinate (2,1).