Answer
Local maximum: $(-1.291,5.303)$
Local minimum: $(1.291,-3.303)$
Work Step by Step
We are given the function:
$f(x)=x^3-5x+1$.
Graph the function:
A local maximum is $(-1.291,5.303)$.
A local minimum is $(1.291,-3.303)$.
The function is increasing on the intervals:
$(-\infty,-1.291)\cup(1.291,-3.303)$
The function is decreasing on the interval:
$(-1.291,1.291)$
