- Given
the function:
_{}

a.) Find all critical values

Answer______________________

b.) Show how to use the second derivative test or the first derivative test to determine if the critical values are a maximum or minimum.

Answer______________________

c.) Find the absolute maximum and minimum values on the interval [-2,2]

Answer______________________

- Given
the function
_{}find the following values.

a.) Vertical Asymptotes

Answer______________________

b.) Horizontal Asymptotes

Answer______________________

c.) Interval where f(x) increases.

Answer______________________

d.) Interval where f(x) is concave up.

Answer______________________

- The
sales S of a certain book is found to follow the formula
_{}where p is the price asked. The revenue is a product of the price and the amount sold.

a.) Give the Revenue as a function of the price asked.

Answer______________________

b.) What price will yield the maximum revenue?

Answer______________________

c.) What price(s) will yield the minimum revenue?

- Given
the function:
_{}

Find the zero using

Be sure to list the first 5 iteration:

- Suppose
that during a trip, the distance traveled away from home
*s*miles at time*t*hours is modeled by the function_{}

What is the velocity at t = 2?

Answer:__________________

What is the acceleration at t = 2?

Answer:__________________

Verify that there must be a time between t = 0 and t = 2 where the speed is 8 mph.

Answer:__________________

At what time did that occur?

Answer:__________________

- An open rectangular box is created by cutting square corners from a sheet of cardboard that is 12 by 15 inches.

a.) Find the maximum volume possible

Answer:__________________

b.) What would be the largest volume possible if you were restricted to cutting squares that are between 2.5 and 3 inches?

Answer:__________________

1. Use the data points to plot a linear regression:

(1900,3.5), (1950,4.5),(2000,6)

2. After performing a quadratic regression, you obtain the formula y(x) = x(x-2). Find the area under the curve between 0 and 2 in the following manners:

a.) Estimate the area with 4 rectangles of equal width.

b.) Estimate the area with 4 rectangles using x1=.5, x2=1 x3=1.25 and x4=2 and Δx1=1, Δx2=.25, Δx3=.25, Δx4=.5 Draw a picture of this approximation.

c.) If and show how you might find the exact area as a limit as n goes to infinity of a sum of equally spaced rectangles of width 2/n

d.) Verify this by finding a definite integral.

e.) Check this value in the calculator

3. Evaluate the integrals:

4. Evaluate the integral using a geometric approach

5. Explain what is wrong with this integral.

6. Evaluate the integral using substitution.

What is the average value of over the interval [-2,3]?

7. If the acceleration a(t) = -10 and v(0) = 30, find the velocity v(t).

What is the displacement from t = 0 to t = 4?

What is the distance traveled from t = 0 to t = 4?

8. Sketch the curve y = 1/t and shade the region under the curve whose area is ln3.

If ln a = 2, find a.

Give an integral whose area is 2.