Attachment 29065

Where (what interval) on f is the graph concave up?

This IS the graph of the 2nd derivative. So to answer this question, perhaps we need the graph of the function. So do we take the 2nd integral and graph?

Answer: why?

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- August 26th 2013, 06:53 PMJason762nd Derivative Chart
Attachment 29065

Where (what interval) on f is the graph concave up?

This IS the graph of the 2nd derivative. So to answer this question, perhaps we need the graph of the function. So do we take the 2nd integral and graph?

Answer: why? - August 26th 2013, 07:06 PMchiroRe: 2nd Derivative Chart
Hey Jason76.

Hint: The definition of concave up is when d^2y/dx^2 > 0. From here:

Second derivative test - Wikipedia, the free encyclopedia - August 26th 2013, 08:24 PMJason76Re: 2nd Derivative Chart
- August 26th 2013, 08:36 PMchiroRe: 2nd Derivative Chart
You said in your original post that the function was concave up.

Remember you are talking about the sign of the second derivative (and your graph is of the second derivative not the actual function). - August 26th 2013, 08:53 PMJason76Re: 2nd Derivative Chart
- August 26th 2013, 09:29 PMchiroRe: 2nd Derivative Chart
You are looking at the sign of the second derivative at a point (or an interval as you are doing).

Don't look at the concavity of the 2nd derivative: just look at the sign of the derivative.

Also note that a function can have segments that are both concave up and concave down in different regions.