Math 142 In Class Review for Final

1. Give the basic function and list the transformations which result in f(x).

a) b)

2. Demand for a product is 400 units when the price per unit is $30. Each increase of $2 in the price causes demand to decrease by 40 units. Fixed costs are $600 and the marginal cost per unit is $20. Find the cost, revenue, and profit functions. At what quantity is profit a maximum?

3. How long will it take an investment to double if interest is 6% compounded a) monthly?

b) continuously?

4. What is the interest rate if $1000 grows to $1256 in 4 years and interest is compounded continuously?

5. Solve for x if

6. Find all asymptotes of

7.

a) At what values of c does not exist?

b) At what x values is f not continuous?

c) At what x values is f not differentiable?

8. Find the derivative of each function.

a)

9.

a)Find any local extrema of f.

b) Find any inflection points of f.

10. g(x)=f(x)lnx f(1)=0, f’(1)=1 and f”(1)=2. Find g’(x), g’(1), g”(x) and g”(1). What does the 2^nd derivative test say about g at x=1?

11. Find the equation of the tangent line to at x=2.

12. Find the antiderivatives.

a) b) c) d)

13. A demand equation is where p is the price per unit and f(p) is the quantity. Find E(p). Is demand elastic or inelastic when p=27? Will revenue increase or decrease if p increases from 27 to 30? Find the approximate change in demand if p increases from 27 to 30. Do the same if p increases from 125 to 130.

14. A cost function is . Use fnint to find the average value of the cost for x between 0 and 50.

Find the average cost per unit when x=50.

15. , and g(0)= 5. Find g(t).

16. A person runs miles per hour where t is in hours. How far does the person run between t=0 and t=2.5 hours? What is the average velocity for this time period?

17. Find the left and right hand Riemann sums for v(t) of problem 16 using 5 equal subintervals. What is the limit of these sums as the number of equal subintervals approaches infinity?

All suggested problems in sections 8.1-8.3