Algebra homework help. 1. Find derivatives of the following functions. Be sure to show all work. Do not simplify your work. (2

points each)

a) z(x) = e (x 7x)

x

2 3 +

b) g(x) = √x + 3 + ln(x)

2. (2 points each) A ball is thrown from the top of a building and its height (in feet) as a function of time t

(in seconds) can be modeled by the function:

h(t) = − 16t 28t 144.

2 + 1 +

a) How tall is the building from which the ball is thrown?

b) The velocity function v(t) can be found by taking the derivative of the height function. Find v(t).

c) What is the ball’s initial velocity?

d) At what time does the ball reach its highest point?

e) What is the maximum height the ball reaches? (1 point)

3. You run a business with a cost function C(q) = 14 + and a revenue function R(q) = +20.

q

40 √q

a) State the profit function for your business. (1 point)

b) Find the production level q that maximizes profit. (2 points)

c) Use a derivative test to show that your answer in part b) is in fact a maximum. (2 points)

4. You are building a fence to hold 3 different kinds of animals (each type of animal must be kept apart).

You need the total area enclosed by the fence to be 1000 square feet. How long should each side of the

fence be so that the material to build the fence is minimized? See diagram below (not necessarily to

scale!). (4 points)

5. True or False. (1 point each)

a) Minimizing total cost will maximize profit.

b) If the demand function is q = 10p

3

, and price is set to $1, you can increase revenue by increasing price.

c) If f″(107) = 0 then f(x) has an inflection point at x = 107.