math 271 test 3

Name

1. For the following functions, determine the locations and of relative extrema, either minimum or maximum, and their values.

a.

b.

c.

d.

e.

2. The total profit P(x) from the sale of x units of a product is given by for x between 0 to 10.

a. Find the units of x to be sold to maximize the profit

b. What is the maximum profit?

3. Graph the following function and its tangent line at the given point – use meta-calculator or Desmos function grapher

a.

b. at (1,2)

4. Given For the following functions, determine the locations and of absolute extrema, either minimum or maximum, and their values.

a.

b.

c. with domain [ 1, 4]

5. Answer the following indefinite integrals:

a. x

b. x

c.

d.

e. u

6. Answer the following definite integrals:

a.

b.

c.

d.

e.

7. A company has its profit function P(t) define since its inception for a given year . By experience, they compute

a.

b. what’s its first year profit? (that is, t = 1)

c. what’s long term projection of its profit? That is = ?