Question

Find the greatest and the least values of the following functions.
$y=x^5-x^3+x+2$ on the interval [-1, 1].

Answer 1

$y=x^5-x^3+x+2$

$\frac{dy}{dx}=5x^4-3x^2+1=0$

$5x^4-3x^2+1=0$,has imaginary roots, ,hence there is no absolute maximum for this function.

$f(-1)=1$ is the local minimum in the interval $[-1,1]$

$f\left(1\right)=3$ is the local maximum in the interval $[-1,1]$