# Math 1501

## Quiz 5

Sept 30, 1999

Tom Morley

Name: ____________________________

*Don't Panic*

### Open Book and Notes. You have 30 minutes. Carefully explain your proceedures and answers

### 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

##### a)

##### b)

This is the formula you use