Take Home Quiz 3

Part I, Sections 2.6-2.8

1. Using the limit definition, find the derivative of .There is a line which is tangent to the graph at x=0. What is this line?

2.

b) Find m and c so that f is continuous and differentiable at x=1.

c) Does the 2nd derivative of f exist at x=1? Why or why not?

3. Find any local max, local min and inflection points of each function. Show all work and sign charts. You may use the power rule.

a)

b)

c) Use your answer to b and the shift rule to find the local max, min and inflection points of h.

Take Home Quiz 3 Part II Sections 3.1-3.3

4. Find f '(x) and f "(x) for . Use these and the fact that to sketch the graph. Show your derivatives, sign charts, local max or min, and inflection point(s).

5. Find using

a) the quotient rule.

b) the power rule but rewrite f(x) as a sum of powers of x first.

6. Simplify and then find f '(x).

7. Find the derivative of each.