Math 450 3rd week Quiz 2st supplement. You must show the work in order to justify the answers. (Total 100)
1. Given the Function:
a. Find the domain of
b. Find the x values for which is discontinuous.
c. Find
d. Find
2. Find the derivatives .( Do not simplify.)
a.
b.
c.
d.
e.
3. The weekly revenue for a company that produces a single product, is given by the function
where x is the level of production (i.e., # of units produced).
a. Find the marginal revenue function
b. Find the level of production for which the revenue function
is maximum.
Find the maximum value of
c. Find the marginal revenue when x = 10
d. Write the equation of the tangent line to the graph of y = R(x) when x = 10.
4. Given the function
a. Find the critical points , the intervals of increase and decrease and the relative maximum and minimum of the function.
b. Find the intervals of concavity (up or down) and the inflection points of the function.
5. Find the absolute maximum and the absolute minimum of the function f(x) over the interval [0,4].
6. Find an antiderivative for the given indefinite integrals.
a.
b. (Use a substitution.)
7. Evaluate the given definite integrals.
a.
b. (Use a substitution)
