6. Graphical Applications of Derivatives

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

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

Find the critical points of the given function.

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

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

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

Find the critical points of the given function.

$g(x)=\(\frac\)13x^3-\(\frac\)12x^2-12x$

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

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

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

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

Find the critical points of the given function.

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