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?

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- Nov 6th 2012, 10:27 PMmettlerSecond 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? - Nov 7th 2012, 05:27 AMSorobanRe: Second Derivative Interpretation
Hello, mettler!

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

Quote:

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

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

Normally you can find this by getting $\displaystyle f''(x) = 0$, right?

But how do I take that function = 0?

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

The equation cannot be solved by elementary means.

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