Associated Topics || Dr. Math Home || Search Dr. Math

### Does f Have a Local Extrema at x = 0?

```Date: 07/10/2003 at 16:29:40
From: Sara
Subject: I'm horrible with trig

f(x) = (x^3)/6 + (x^2)/2 + cosx - 1

Does f have a local extremum at x = 0?
```

```
Date: 07/10/2003 at 17:54:01
From: Doctor Jaffee
Subject: Re: I'm horrible with trig

Hi Sara,

If a function is differentiable for all values of x (which your
function is), all that you have to worry about is if the first
derivative is equal to zero and the second derivative isn't.

The reason is that if the first derivative equals zero, then the
tangent line is horizontal, so the point is either a maximum, a
minimum, or possibly an inflection point. If the second derivative is
zero, then the point is an inflection point.

So, calculate f'(0) and f"(0) and you should have the answer to your
question.

Give it a try and if you want to check your solution with me or if you
have difficulties or other questions write back to me and I'll try to

Good luck,

- Doctor Jaffee, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search