1) [20 pts] Consider the following function.

a) Find all of the critical points and inflection points ALGEBRAICALLY. Show all the work as if you did not have a graphing calculator.

b) Find the largest intervals for which the function is increasing, decreasing, concave up and concave down. Show all the work as if you did not have a graphing calculator.

c) List the value and location of each relative max and min, and list the location of each inflection point. Show all the work as if you did not have a graphing calculator.

d) Find the location and value of both the absolute max and min on [-2,1]. Show all your work.

e) Find the location and value of both the absolute max and min on [-4,-2]. Show all your work.

2) [10 pts]

a) For the function graphed above, estimate the location and value of each relative max and min, and estimate the location of each inflection point.

b) Find any closed interval [a,b] such that the absolute max occurs at a relative max, and the absolute min occurs at a.

c) Find any closed interval [a,b] such that the absolute max occurs at b, and the absolute min occurs at a relative min.

3) [10 pts] The Vista Cable Co. currently has 2000 subscribers who are each paying a monthly price of $20. A survey reveals that there will be 50 more subscribers for each $0.25 decrease in the price. At what price will the maximum revenue be obtained and how many subscribers will there be? (HINT: Let x be the number of $.025 decreases and make a revenue equation)

4) [10 pts] Find by implicit differentiation and find the slope of the tangent at (1, 2)

5) [10 pts] As a snowball rolls down a hill, it’s volume is increasing at a rate of 408 when the radius is 3 inches. How fast is the radius changing at this moment? Assume the snowball is spherical, and remember that V=(4/3)*pi*r^3 for a sphere.

6) [10 pts] A company’s marginal cost function is shown below. How much does it cost to produce 150 items, if fixed costs are $100.00?

7) [15 pts] Let estimate the velocity of an object in ft/sec.

a) Estimate the distance traveled from t = 2 to t = 5 seconds by finding the right hand sum where n=6. (in other words, use 6 rectangles).

b) Estimate the distance traveled from t = 2 to t = 5 seconds by finding the left hand sum where n=6. (in other words, use 6 rectangles).

c) What do the solutions to a) and b) tell us about our distance traveled?

d) How can we get a better estimate?

8) [10 pts] Find each antiderivative.

a)

b)

9) [5 pts] Find the following definite integral. (Hint: Draw a sketch.)