Is $f(x)=(x^2-6x-12)/(x+2)$ increasing or decreasing at $x=1$ ?

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Answer 1 · 2016-03-13T23:51:51

Increasing (with slope $5/9$ )

$f(x) = (x^2-6x-12)/(x+2) = ((x^2+2x)-(8x+16)+4)/(x+2) = x-8+4/(x+2)$

So:

$f'(x) = 1-4/(x+2)^2$

and:

$f'(1) = 1 - 4/(1+2)^2 = 1 - 4/9 = 5/9 > 0$

So $f(x)$ is increasing at $x=1$

graph{(x^2-6x-12)/(x+2) [-8.59, 11.41, -7.28, 2.72]}

Is f(x)=(x^2-6x-12)/(x+2)f(x)=(x^2-6x-12)/(x+2) increasing or decreasing at x=1x=1?