Local Minimums and Maximums

I'm not really understanding how to do this problem.

Quote:

For $\displaystyle x$ $\displaystyle \in [-13,14]$ the function $\displaystyle f$ is defined by

$\displaystyle

f(x)=x^7(x+6)^2$

On Which two intervals is the function increasing?

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and

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Find the region in which the function is positive?

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Where does the function achieve it's minimum?

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My first step is to take the derivative and find the critical numbers.

But what I don't get is:

What does this mean?

Quote:

For $\displaystyle x$ $\displaystyle \in [-13,14]$

Is a different way of saying find where the function is increasing?

Quote:

Find the region in which the function is positive?