# For what values of x is f(x) concave up and down? Given the graph.Here is the graph: http://imgur.com/FdQCVThe graph above shows f(x) a quartic, so the derivative of it would be a cubic. What...

For what values of x is f(x) concave up and down? Given the graph.

Here is the graph:

http://imgur.com/FdQCV

The graph above shows f(x) a quartic, so the derivative of it would be a cubic. What points do I use to find what values are concave up and down?

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### 2 Answers

For what values is f(x) concave up and concave down.

The function is similar to this:

-1/12x^2(x+3.5)(x-4.5)

In the problem, the f(x) axis is not labelled, and the x-intercepts are not labelled. So I believe you are supposed to *approximate* the inflection points. (The graph I have is not as symmetric as the picture in the link)

**Here the graph is concave down on `(-oo,-1)` , concave up on `(-1,2)` , and concave down on `(2,oo)` **

Wouldn't we have to change the original graph to the derivative to find the concavity?