# Math 1501

## Quiz 5Sept 30, 1999Tom MorleyName: ____________________________

### Problem 1 (5 points)

Show below is a plot of f(x) identify all critical points. Draw a picture of f'(x), using information about increasing, decreasing, and concavity.

#### Calculations

So here is a plot of the function as given (blue),
and its derivative. The roots of the derivative are
the critical points.

### Problem 2 (6 Points)

The derivatives of the follwing 3 functions on the left are in a different order on the right. Match up the functions and the derivatives.

#### Calculations

So. On the left A, B, C, and 1,2,3 on the right,
match up as: A3, B1, C2

`Show[GraphicsArray[{    {First[p4],Last[p2]},    {First[p2],Last[p3]},    {First[p3],Last[p4]}}]]`

### Problem 3 (10 Points)

a) Use differentials to approximate .

b) Find a function f(x), such that is a root. Use a function that will be useful for Netwon's method. (Note: This is different from the function in part a). Using the answer to a) as the original guess, do ONE step of Newton's method.

#### Calculations

##### b)

This is the formula you use