# Homework Help: Inflection Points

1. Feb 28, 2008

### undrcvrbro

1. The problem statement, all variables and given/known data
Explain how you can locate the local maxima and minima for the graph of y=f '(x) by examining the graph of y=f(x).

2. Relevant equations

3. The attempt at a solution
If there is an inflection point on the graph of y=f(x) at x=c, then f(x) must change concavity at x=c. Consequently, f '(x) must change from increasing to decreasing or from decreasing to increasing at x=c, and x=c is a local extremum for f '(x). If there is an inflection point on the graph of y=f(x) at x=c, then f(x) must change concavity at x=c. Consequently, f '(x) must change from increasing to decreasing or from decreasing to increasing at x=c, and x=c is a local extremum for f '(x).

I must be missing something. Don't you need to know the second derivative in order to know where the inflection points actually are?

2. Feb 28, 2008

### foxjwill

Maybe they're just asking you to locate, by actually plotting y=f(x), its inflection points.

3. Feb 29, 2008

### HallsofIvy

Well, not by plotting a specific function, but just explaining that at an inflection point, the graph changes from "convex up" to "convex down". Typically we find the second derivative, in order to find the inflection points, in order to tell where the curve changes convexity. The point of this problem is we can do it, at least roughly, the other way. If we look at the graph and can see where it changes convexity, we can see where the inflection points are (and, so, where the second derivative is 0).

4. Feb 29, 2008

### undrcvrbro

oh

ohh alright. thanks ivy.