Question

What are the local extrema, if any, of `f (x) =x^2-2x+4`?

Answer 1

`f(1) = 3` is a local minimum.

Explanation:

`f'(x) = 2x-2`

Critical number `x=1`.

`f'(x) < 0` for `x < 1` and `f'(x) > 0` for `x > 1`, so `f(1) = 3` is a local minimum.