- 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.