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Suppose the derivative of a function $f$ is below. On what interval is $f$ increasing?

$$ f'(x) = (x+1)^4(x-5)^3(x-7)^6 $$

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Where does the second derivative come in? – Arturo Magidin Nov 28 '11 at 2:10
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Why use the Second Derivative Test (en.wikipedia.org/wiki/Second_derivative_test)? The hint/answer provided below should answer your questions. – JavaMan Nov 28 '11 at 2:14

1 Answer

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$f(x)$ is increasing wherever $f'(x) > 0$. Thus, it follows that $f(x)$ is increasing wherever:

$$(x+1)^4 (x-5)^3 (x-7)^6 > 0$$

I hope you can take it from here.

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