Please work out each of the given
problems. Credit will be based on
the steps that you show towards the final answer.
Show your work.
PROBLEM 1 Please answer the following true or false. If false, explain why or provide a counter example. If true, explain why or state the proper theorem.
A) Suppose that f(x) and g(x) are differentiable inverse functions, and f '(2) = 3. Then g'(2) = 1/3.
B) If f is a differentiable function such that both f and f ' are positive for all x, then g(x) = ln(f(x)) is increasing for all values of x.
PROBLEM 2 Calculate the derivatives of the following functions.
PROBLEM 3 Find the following integrals
PROBLEM 4 Let f(x) = 2x3 + 4x + 5
that f(x) has an inverse.
PROBLEM 5Show that
Extra Credit: Write
down one thing that your instructor can do to make the class better and one
thing that you do not want changed with the class.
Questions, Comments and Suggestions: