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37. Determine the maximum and minimum points of the curve y  4x  15x  18x  by
using the first derivative test.

38. The total revenue function and cost function of a company that produced car components

are   0.2R x  x  2 80x and   0.1x  40x  6000 respectively where x is the number

2
C
x
of unit components produced. Find
(a) the total profit function
(b) the demand function

(c) the profit obtained when 1000 unit components are sold

(d) the number of units component to be produced to minimizes the cost. Hence, find
the minimum cost and price per unit components.

39. The equation of a curve is given by y  3 2x y  3 3. Find the equation of the tangent to the

curve at = 1.

40. An electronic company is producing microchips for local market. The company that

C
average cost function   x and the demand function ( ) where is the quantity of
20x  10000
microchips are given by   x  and   100 0.01 .p x   x Find
C
x
(a) The total cost function and fixed cost
(b) The total revenue function

(c) The total profit function

(d) The price per microchip when the profit was maximized. Hence, calculate the
maximum profit.

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41. The curve   x  ax  bx c has a maximum point at (2,10). Find the values of , and
f
if f passes through point (0,2).

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42. (a) Find the local maximum and minimum point of the curve y   6x  9x  2.