What are the local extrema, if any, of f (x) =(x+1)^7/2?

Nov 22, 2015

$f ' \left(x\right) = \frac{7}{2} {\left(x + 1\right)}^{6}$ is never undefined and is $0$ only at $x = - 1$.
So, the only critical number is $- 1$.
Since $f ' \left(x\right)$ is positive on both sides of $- 1$, $f$ has neither a minimum nor a maximum at $- 1$.