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 1 
(b) Find the equation tangent to the curve x  2 3y  2 6y at point 1,  .

 2 

43. A company which produces cakes and find that the total cost function and the demand


function are   1000 10C x   x and   100 x respectively where x is the number of
D
x
cakes produced.
(a) Construct the total revenue function and find the number of cakes that should be

produced in order to maximize the revenue.
(b) Determine the profit and the number of cakes that should be produced in order to

maximize the profit. Hence, find the maximum profit.

(c) Compute the maximum profit if each cake is taxed at RM5.

44. (a) Find the local maximum or minimum point using the second derivative test for the

curve y  9x 3x  2  1 where > 0.

(b) Find the gradient of the tangent line to the curve x  2 y  2 10 at = 1, where

> 0.

2
45. The revenue function, (in RM) for sales of x units of a product is   x   ax  bx, where
R
and are constants. Given that the sale that maximizes revenue is 300 units and the

maximum revenue is RM 27,000.
(a) Find the values of and

(b) Find the demand function of the product. Hence, find the price of a unit of the

product when the revenue is maximum.
2
(c) Given the cost function   0.05C x  x  9x  2500. Find the maximum profit.

ANSWERS

2
1. (a) R   400q  q  2q

2
(b) C   2q  q  4q  400
(c) Maximum profit is RM 9401