In Class Exam 2 Review Math 131

1. What is the limit definition of the derivative with respect to x as a function?

Write the limit definition for the derivative of .

2. Find the equation of the tangent line to f(x) at (a, f(a)).

3. Determine any and all x-values where the function is not differentiable.

In part c, what change could be made to make f continuous at x=3? Then would it be differentiable?

4. is the tangent line to g(x) at x=1.

Find the tangent line to h(x) at (1, h(1)).

5. Find f '(x) :

6. Find any and all local max, min and inflection points of

a) .

b)

7. If f(t) is distance and t is time and f(t) is increasing at an increasing rate then v(t) is _______ and a(t) is _______________.

When v(t) has a maximum, a(t) is ______________ and the graph of f(t) has ____________.

If g '(x) is negative and is becoming more and more negative then g is ____________

and _________________.

8. Find f '(t).