# Derivative and second derivative question

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
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

$f(x)$ is increasing wherever $f'(x) > 0$. Thus, it follows that $f(x)$ is increasing wherever:
$$(x+1)^4 (x-5)^3 (x-7)^6 > 0$$