Find Local Maxima/Minima of y=f'(x) from y=f(x)

[undrcvrbro]

Homework Statement

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).

Homework Equations

The Attempt at a Solution

In the back of the book the answer reads:
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?

 

[foxjwill]

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

 

[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).

 

[undrcvrbro]

oh

ohh alright. thanks ivy.