1. Find the stationary values of the following (check whether they are relative maxima or minima or inflection points ssuming the domain to be the set of all real numbers:
(a) y = 5x2 + x (b) y = 3x2 - 6x + 2
2. Find the stationary values of the following (check whether they are relative maxima or minima or inflection points), assuming the domain to be the interval [0, ∞):
(a) y = 1/3x3 - x2 + x + 10
(b) y = -x3 + 4.5x2 - 6x + 6
3. Find the second and third derivatives of the following functions:
(a) 7x4 - 3x - 4 (b) (1+x)/(1-x) (x≠1)
4. Find the relative maxima and minima of y by the second-derivative test:
(a) y = x3 + 6x2 + 9
(b) y = 2x/1-2x (x≠1/2)
5. A firm has the following total-cost and demand functions:
C = 1/3Q3- 7Q2 + 111Q + 50
Q= 100 - P
(a) Does the total-cost function satisfy the coefficient restrictions of (9.5)?
(b) Write out the total-revenue function R in terms of Q.
(c) Formulate the total-profit function Π in terms of Q.
(d) Find the profit-maximizing level of output Q.
(e) What is the maximum profit?
6. Find the value of the following factorial expressions:
(a) 8! (b)6!/4!