1)
Differentiate the following functions,
(a) f(x)=1/5 x^5-1/3 x^3+5
(c) y=(3x^2-9)/x
(c) y = ln ?(3x^5+8x-5)?^2
2. Find the critical points for y=x^3-3x+1 and determine whether the critical points are minimum, maximum or inflection.
3. Entrepreneur of a product estimates that when q units of his items produced every month, the average total profit (in thousand RM) is
P ¯(q)= -1.125q+45-200/q.
Find the company's maximum profit.
4. Given f(x,y)=3x^3 y^2. Then find:
(i) f_x (-1,2)
(ii) f_y (-2,1)
5. Using LaGrange Multipliers, find x and y that will maximize
f(x,y)=3x^2+xy+2ysubject to the constraint x + y = 200.
6. Integrate:
(a) ∫¦?2x(x^2-3)^5 ?dx
(b) ∫_4^10¦√(5x+1 ) dx
7. The demand functions for a product is given by p=200-q^2, where p is the price per unit and q is the quantity. If the supply function is given by p=6q+160, find the consumer's surplus and producer's surplus under market equilibrium.