This is an actual M403K midterm given on Thursday, September 26, 1991. On that test I allowed a ``crib sheet'' and a non-graphing calculator.

The syllabus has changed some in 9 years, so this exam doesn't cover
exactly the same material as our first midterm will. In particular, problem
3 is Chapter 2 material, which will be tested in the *second* midterm.

**Problem 1. Tangent lines**

Consider the curve Find the equation of the line that is tangent to this curve at the point (1,-1).

**Problem 2. Limits and continuity**

Consider the function

a) Find , , and , if they exist.

b) Is *f*(*x*) continuous at *x*=2? Why or why not?

**Problem 3. Graphs and optimization**

Consider the function .

a) For what values of *x* is this function increasing? For what
values of *x* is it decreasing?

b) On the interval [-1,3], find the maximum and minimum values of
*f*(*x*)
(and where these values occur).

**Problem 4. Taking derivatives**

Take the derivatives, with respect to *x*, of the following functions:

a)

b)

c)

d)

**Problem 5. Taking limits**

Evaluate the following limits:

a)

b)

c)

d)