Reference no: EM131397160
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!
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