What are the critical values, if any, of f(x)= (x+1)^2 /(-x^2 - x)?

Jun 24, 2018

No critical values

Explanation:

Note that

${\left(x + 1\right)}^{2} / \left(- {x}^{2} - x\right) = {\left(x + 1\right)}^{2} / \left(- x \left(x + 1\right)\right) = - \frac{x + 1}{x} = - 1 - \frac{1}{x}$
for $x \ne - 1$
so

$f ' \left(x\right) = \frac{1}{x} ^ 2 \ne 0$