# Thread: Local Minimums and Maximums

1. ## Local Minimums and Maximums

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

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?
For $\displaystyle x$ $\displaystyle \in [-13,14]$
Is a different way of saying find where the function is increasing?
Find the region in which the function is positive?

2. $\displaystyle \in$ means is contained in. So $\displaystyle x\in [-13,14]$ reads $\displaystyle x$ is contained in the interval $\displaystyle [-13,14]$.

$\displaystyle f(x)$ positive doesn't mean $\displaystyle f(x)$ is increasing.
$\displaystyle f(x)=\cos(x)$ on the interval $\displaystyle (0,\frac{\pi}{2})$ is positive but decreasing.