91Ó°ÊÓ

Use either (3) or (4) to compute the derivative of the given function. Find the points on the graph of \(f\) at which \(f^{\prime}(x)=0 .\) Interpret your answers geometrically. $$ f(x)=x^{3}-3 x^{2}-9 x $$

Find the real zeros of the given function \(f\). $$ f(x)=x^{4}-1 $$

A printed page will have 2 -in. margins of white space on the sides and 1 -in. margins of white space on the top and bottom. The area of the printed portion is \(32 \mathrm{in}^{2}\). Determine the dimensions of the page so that the least amount of paper is used.

Sketch the region in the \(x y\) -plane that is bounded between the graphs of the given In Problems 41-44, sketch the region in the \(x y\) -plane that is bounded between the graphs of the given $$ y=-x+4, y=x^{2}+2 x $$

Determine which of the given lines are parallel to each other and which areperpendicular to each other. (a) \(3 x-y-1=0\) (b) \(x-3 y+9=0\) (c) \(3 x+y=0\) (d) \(x+3 y=1\) (e) \(6 x-3 y+10=0\) (f) \(x+2 y=-8\)

Find the real zeros of the given function \(f\). $$ f(x)=2-\sqrt{4-x^{2}} $$

Use either (3) or (4) to compute the derivative of the given function. Find the points on the graph of \(f\) at which \(f^{\prime}(x)=0 .\) Interpret your answers geometrically. $$ f(x)=x^{4}-\frac{4}{3} x^{3}+2 $$

Sketch the region in the \(x y\) -plane that is bounded between the graphs of the given In Problems 41-44, sketch the region in the \(x y\) -plane that is bounded between the graphs of the given $$ y=2 x-2, y=1-x^{2} $$

Find an equation of the final graph after the given transformations are applied to the graph of \(y=f(x)\). the graph of \(f(x)=1 / x\) reflected in the \(y\) -axis, then shifted left 5 units and down 10 units

In Problems 41 and 42 , sketch the graph of the \(\operatorname{sum} f\) \(+g\). $$ f(x)=x, g(x)=|x| $$