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

Feb 21, 2017

$f \left(1\right) = 3$ is a local minimum.
$f ' \left(x\right) = 2 x - 2$
Critical number $x = 1$.
$f ' \left(x\right) < 0$ for $x < 1$ and $f ' \left(x\right) > 0$ for $x > 1$, so $f \left(1\right) = 3$ is a local minimum.