Question

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

Answer 1

The function has no local extrema.

Explanation:

`f'(x) = 7/2(x+1)^6` is never undefined and is `0` only at `x=-1`.

So, the only critical number is `-1`.

Since `f'(x)` is positive on both sides of `-1`, `f` has neither a minimum nor a maximum at `-1`.