91Ó°ÊÓ

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

Finding an Equation of a Tangent Line In Exercises \(73-80,\) (a) find an equation of the tangent line to the graph of \(f\) at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results. $$ y=\left(4 x^{3}+3\right)^{2},(-1,1) $$

Finding an Equation of a Tangent Line In Exercises \(73-80,\) (a) find an equation of the tangent line to the graph of \(f\) at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results. $$ f(x)=\left(9-x^{2}\right)^{2 / 3},(1,4) $$

Determining Differentiability In Exercises \(75-80\) , describe the \(x\) -values at which \(f\) is differentiable. $$ f(x)=\left|x^{2}-9\right| $$

Horizontal Tangent Line In Exercises \(73-76\) , determine the point(s) at which the graph of the function has a horizontal tangent line. $$ f(x)=\frac{x-4}{x^{2}-7} $$

Tangent Lines Find equations of the tangent lines to the graph of \(f(x)=(x+1) /(x-1)\) that are parallel to the line \(2 y+x=6 .\) Then graph the function and the tangent lines.

Determining Differentiability In Exercises \(75-80\) , describe the \(x\) -values at which \(f\) is differentiable. $$ f(x)=(x+4)^{2 / 3} $$

Finding an Equation of a Tangent Line In Exercises \(73-80,\) (a) find an equation of the tangent line to the graph of \(f\) at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results. $$ f(x)=\sin 2 x,(\pi, 0) $$

Finding Equations of Tangent Lines Sketch the graphs of \(y=x^{2}\) and \(y=-x^{2}+6 x-5\) , and sketch the two lines that are tangent to both graphs. Find equations of these lines.

Tangent Lines Show that the graphs of the two equations $$y=x\( and \)y=\frac{1}{x}$$ have tangent lines that are perpendicular to each other at their point of intersection.