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