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20. Consider the curve y  x  2x  2.
(a) Determine the stationary points of the above curve and hence determine whether

the stationary points are maximum or minimum points.
(b) A point (2, ) is on the curve. Determine the value of , and hence find the equation

of the tangent line at the point.

21. The demand function for a product is   200 2p x   x and the average cost function is

200
C   0.4x  x  8 where is the number of units produced. Find
x
(a) the cost, the revenue and the profit function

(b) the level of output and the price at which the profit is maximized

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22. The revenue function for the sales of x unit of product is   x   ax  bx ,where and
R
are constants. If the optimal sale that maximizes revenue is 10 units, and the maximum

revenue is RM 500, find the value of a and . Hence, find the price when the revenue is

maximum.

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23. The equation of a curve is y  10x  ax  12x b where and are constants. The curve
,
has a minimum value of 6 at = 1.
(a) Find the values of and
(b) The gradient at the point ( , ) on the curve is 12, where > 0. Find the equation

of the normal line to the curve at M.

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24. ( , ) is a point on a curve y  2x  3 5x 2  with > 0. Given the tangent line to the
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curve at the point is parallel to the line = , find the values of and . Hence find the
equation of the normal line at the point .

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x
25. At a particular point of the curve y  2x   , q the equation of the tangent is
= 3 − 5. Find the value of the constant .