Critical Numbers and Graphing from Formulas

Consider the function $k$ defined by $\fe{k}{t}=\sqrt[3]{t^8}-256\sqrt[3]{t^2}$.

Create an increasing/decreasing table for $k$.

Consider the function $k$ defined by $\fe{k}{t}=\sqrt[3]{t^8}-256\sqrt[3]{t^2}$.

State each local minimum and maximum point on $k$.

Consider the function $f$ defined by $\fe{f}{x}=\fe{\cos^2}{x}+\fe{\sin}{x}$ over the restricted domain $\cinterval{0}{2\pi}$.

What are the critical numbers of $f$? Remember to show all relevant work! Remember that your formula for $\fe{\fd{f}}{x}$ needs to be a single, completely factored, fraction!

Consider the function $f$ defined by $\fe{f}{x}=\fe{\cos^2}{x}+\fe{\sin}{x}$ over the restricted domain $\cinterval{0}{2\pi}$.

Create an increasing/decreasing table for $f$.

Consider the function $f$ defined by $\fe{f}{x}=\fe{\cos^2}{x}+\fe{\sin}{x}$ over the restricted domain $\cinterval{0}{2\pi}$.

State each local minimum and maximum point on $f$.

Consider $\fe{g}{t}=\frac{t+9}{t^3}$. Find (and completely simplify) $\fe{\sd{g}}{t}$ and state all numbers where $\fe{\sd{g}}{t}$ is zero or undefined. Then construct a concavity table for $g$ and state all of the inflection points on $g$.