# Homework Help: Urgent Help Needed - Local Minimum/ maximum question

1. Mar 28, 2012

### chubbyorphan

Hey forum I gotta submit this in a few hours so if anyone could help me with this quick times, you would really be saving me :P

1. The problem statement, all variables and given/known data
Given the following graph of h(x)
I only need help with part b)
which asks for the local minimum or maximum points of the graph

http://i43.tinypic.com/hvyrk4.jpg

3. The attempt at a solution

So basically I realize there's a horizontal tangent at the point h(2)

What I can't decide is if there is neither a minimum nor maximum (my initial thoughts)

but then one part of my book reads for ANOTHER graph:
f'(x) is never zero, so the function has no local maximums or minimums

and we can clearly see that h(x) has a horizontal tangent implying that h'(x) would be zero at h'(2).. so
is the point [2,h(2)] both a local minimum and a local maximum

Is that even possible for a point to be both a local maximum and a local minimum?

if someone could clarify as to why its whichever answer that would be awesome!