5. Graphical Applications of Derivatives

Use the second derivative test to find the local extrema of the given function.

$f\(\left\)(x\(\right\))=\(\frac{x^2-4}{x^2+1}\)$

Use the second derivative test to find the local extrema of the given function.

$g(x)=x^3-6x^2+9x+2$

Use the second derivative test to find the local extrema of the given function.

$f\(\left\)(x\(\right\))=4\(\sin\) x\(\cos\) x$; $0$ < $x$ < $\(\pi\)$