6. Graphical Applications of Derivatives

Find the critical points of the given function.

$g(x)=\frac13x^3-\frac12x^2-12x$

Find the critical points of the given function.

$f(t)=\frac{6t}{t^2+1}$

Find the critical points of the given function.

$f(x)=\sqrt{2-x^2}$

Identify the open intervals on which the function is increasing or decreasing.

$f(x)=3x^4+8x^3-18x^2+7$

Identify the open intervals on which the function is increasing or decreasing.

$f(x)=x^{2/3}(4-x)$

Identify the open intervals on which the function is increasing or decreasing.

$f(x)=xe^{-2x}$

Identify the local minimum and maximum values of the given function, if any.

$f(t)=t^2\ln t$, $t>0$