# Second Derivative Interpretation

• November 6th 2012, 10:27 PM
mettler
Second Derivative Interpretation
I'm given f''(x) = sin(3x)ln(x+5) - xcos(3x)

1. List intervals where f(x) concave up & concave down with justification.

Normally you can find this by getting f''(x) = 0 right? But how do I take that function = 0?
• November 7th 2012, 05:27 AM
Soroban
Re: Second Derivative Interpretation
Hello, mettler!

I've made a few observations . . . that's all.

Quote:

I'm given: $f''(x) \:=\: \sin(3x)\ln(x+5) - x\cos(3x)$

1. List intervals where $f(x)$ is concave up & concave down with justification.

Normally you can find this by getting $f''(x) = 0$, right?
But how do I take that function = 0?

Note that the domain is $x > \text{-}5$

The equation cannot be solved by elementary means.

By inspection, we find that $x = 0$ is a solution.