# Homework Help: Local maxima and minima

1. Mar 30, 2012

### jorcrobe

1. The problem statement, all variables and given/known data
F(x)=(x^2)/(x+1)
Find critical points
Find local maxima & minima

2. Relevant equations
None

3. The attempt at a solution
F'(x) = x(x+2)/(x+1)^2

crit points: -2,0,-1

f(-2) = -4
f(0) = 0
f(-1)=undef

My book is telling me that f(0) is the minima, and f(-2) is the maxima. I see it as the other way around. Which way is right? Explanations? Thank you!

2. Mar 30, 2012

### SammyS

Staff Emeritus
The book is correct.

I suppose you're having trouble because the local maximum is less than the local minimum.

Graph F(x) to see what's happening .

3. Mar 31, 2012

### Ray Vickson

The book is correct. For *local* min/max (as you have here) there are second-order conditions that can be applied: if f'(x0) = 0 and f''(x0) < 0 then x0 is a strict local maximum; if f'(x0) = 0 and f''(x0) > 0, x0 is a strict local minimum. Try these tests on your function.

This does not say anything about *global* max or min, and it does not prevent a local max from being less than a local min, which is the case in this problem.

RGV

4. Mar 31, 2012

### jorcrobe

I'd like to thank you both for your guidance. I will be looking into this further.