How do you find the critical points if $f'(x)=2-x/(x+2)^3$ ?

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Answer 1 · 2015-04-14T16:33:43

You need to solve: $2-x/(x+2)^3 = 0$ Which has no rational and only one real, solution.

If you intended to type: $f'(x) = (2-x)/(x+2)^3$ , the we're in better luck.

A critical number is a value in the domain of $f$ at which the derivative is either $0$ or fails to exist.

It looks as if the domain for the original $f$ was $RR - {-2}$ .

$f'(-2) does not exist, but$ -2 $is not in the domain of$ f#, so it is not a critical point.

$(2-x)/(x+2)^3=0$ when $2-x=0$ which happens at $x=2$ .

Assuming that $2$ is in the domain of $f$ , it is a critical point.

How do you find the critical points if f'(x)=2-x/(x+2)^3f'(x)=2-x/(x+2)^3?