Description
Show all work necessary for your answers.
1. Compute the derivative of each of the following functions.
(a) f(x) = 4√
x −
5
x
3
(b) y =
5x − 4x
2
2x
2 − 4x + 7
(c) f(x) = (5x
3 − 3x + 2) · e
x
(d) y =
7x
2 + 2x
x + ln(x)
2. Suppose that the function f is given by f(x) = 12, 000 + 20x − 0.005x
2
.
(a) If x changes from x = 100 to x = 103, find the following: ∆x, ∆y, and dy.
(b) Estimate the change in y as x changes from x = 100 to x = 103.
(c) To compute ∆y in part (a), you computed that f(100) = 13, 950.
Given your answer to part (a), estimate f(103).
3. The daily cost function for a firm which produces blenders is given by C(x) = 12, 000 + 20x − 0.005x
2
,
where x is the number of blenders produced daily. The derivative of C is given by C
0
(x) = 20 − 0.01x.
(a) Find the average cost of increasing production from x = 100 to x = 110 blenders per day.
(b) Compute C(100) and C
0
(100).
(c) Explain the meaning of C(100) and the meaning of C
0
(100).
4. Suppose that the daily price-demand equation for a raincoat is given by p = 30 − 0.05x. Find the daily
revenue function for the raincoats.
5. Suppose that the daily revenue equation for the production and sale of x personal speakers is given by
the function R(x) = 25x − 0.07x
2 and the daily cost function is given by C(x) = 9000 + 7x + 0.03x
2
. Find
the daily profit function, P(x).
6. Suppose that the daily revenue equation for the production and sale of x skillets is given by
R(x) = 28x − 0.04x
2
0 ≤ x ≤ 700