91Ó°ÊÓ

Finding an Equation of a Exercises \(71-78\) , (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. $$f(x)=\left(9-x^{2}\right)^{2 / 3},(1,4)$$

\(\begin{array}{l}{\text { Using the Alternative Form of the }} \\ {\text { Derivative In Exercises } 69-76, \text { use the the }} \\ {\text { alternative form of the derivative to find the }} \\ {\text { derivative at } x=c, \text { if it exists. }}\end{array}\) \(g(x)=(x+3)^{1 / 3}, c=-3\)

Slope Find all points on the circle \(x^{2}+y^{2}=100\) where the slope is \(\frac{3}{4} .\)

Horizontal Tangent Line In Exercises \(73-76\) determine the point(s) at which the graph of the function has a horizontal tangent line. \(f(x)=\frac{x^{2}}{x^{2}+1}\)

\(\begin{array}{l}{\text { Using the Alternative Form of the }} \\ {\text { Derivative In Exercises } 69-76, \text { use the the }} \\ {\text { alternative form of the derivative to find the }} \\ {\text { derivative at } x=c, \text { if it exists. }}\end{array}\) \(h(x)=|x+7|, c=-7\)

Tangent Lines Find equations of both tangent lines to the graph of the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) that pass through the point \((4,0)\) not on the graph.

$$\begin{array}{l}{\text { Sketching a Graph Sketch the graph of a function } f} \\ {\text { such that } f^{\prime}>0 \text { for all } x \text { and the rate of change of the function }} \\ {\text { is decreasing. }}\end{array}$$

Finding an Equation of a Exercises \(71-78\) , (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. $$f(x)=\sin 8 x,(\pi, 0)$$

Horizontal Tangent Line In Exercises \(73-76\) determine the point(s) at which the graph of the function has a horizontal tangent line. \(f(x)=\frac{x^{2}}{x-1}\)

\(\begin{array}{l}{\text { Using the Alternative Form of the }} \\ {\text { Derivative In Exercises } 69-76, \text { use the the }} \\ {\text { alternative form of the derivative to find the }} \\ {\text { derivative at } x=c, \text { if it exists. }}\end{array}\) \(f(x)=|x-6|, c=6\)