Thread: Concavity

The graph of f(x)= integral from 0 to x (15(t^2) - 2(t^3) + 24)dt is concave up on (a,b). Find b-a.

Okay so I know from the curve sketching lesson in AB calculus that to find concavity you take the second derivative and then set that to 0. Do I take the integral and then take the first derivative, and then the second?

see this thread ...

http://www.mathhelpforum.com/math-he...concavity.html

Hello, abclarinetuvwxyz!

The graph of: . . is concave up on ]
Find

The first derivative is: .

The second derivative is: .

Now where is the graph concave up?
. . Where is positive.

So we have: .

This is true when: .

Therefore, the interval is: .

Thanks very much!