1. The cost function C and the price-demand function p are given. Assume that the value of
C(x) and p(x) are in dollars. Complete the following.
C(x) = x^2/100 + 6x + 1000; p(x) = x/20+25
(a) Determine the revenue function R and the profit function P.
R(x) | = | |
P(x) | = |
(b) Determine the marginal cost function MC and the marginal profit function MP.
MC(x) | = | |
MP(x) | = |
3. Determine the derivative for the given single-term function. When appropriate, simplify the derivative so that there are no negative or fractional exponents. A few helpful rules from algebra are:
(i) x−n =
1 |
x n |
, (ii) x m/n =
n | x m |
.
f(x) = −8x−1/8
f '(x) =
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