# 2nd Derivative Chart

• Aug 26th 2013, 05:53 PM
Jason76
2nd 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: \$\displaystyle (-1, 3)\$ why?
• Aug 26th 2013, 06:06 PM
chiro
Re: 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
• Aug 26th 2013, 07:24 PM
Jason76
Re: 2nd Derivative Chart
Quote:

Originally Posted by chiro
Hey Jason76.

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

Second derivative test - Wikipedia, the free encyclopedia

How does that relate to the shown graph, which is concave down?
• Aug 26th 2013, 07:36 PM
chiro
Re: 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).
• Aug 26th 2013, 07:53 PM
Jason76
Re: 2nd Derivative Chart
Quote:

Originally Posted by chiro
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).

So if the original graph is concave up, then the 2nd derivative is concave down. Why?

Actually, what I'm trying to say: If the 2nd derivative is concave down, then HOW do we know the original one was concave up?? (Nod)
• Aug 26th 2013, 08:29 PM
chiro
Re: 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.