91Ó°ÊÓ

Find an equation of the line that is tangent to the graph of \(f\) and parallel to the given line. \(\begin{array}{ll}\underline{\text { Function }} & \underline{\text { Line }} \\\ \text { } f(x)=\frac{1}{\sqrt{x}} \quad x+2 y-6=0\end{array}\)

A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground (see figure). When he is 10 feet from the base of the light, (a) at what rate is the tip of his shadow moving? (b) at what rate is the length of his shadow changing?

Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. $$ y=\sqrt{\frac{x+1}{x}} $$

Find the derivative of the algebraic function. \(f(x)=\left(3 x^{3}+4 x\right)(x-5)(x+1)\)

Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function \(\quad\) Point \(y=(2 x+1)^{2}\) \((0,1)\)

Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. $$ g(x)=\sqrt{x-1}+\sqrt{x+1} $$

Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function \(\quad\) Point \(f(x)=3(5-x)^{2}\) \((5,0)\)

Find an equation of the line that is tangent to the graph of \(f\) and parallel to the given line. \(\begin{array}{ll}\underline{\text { Function }} & \underline{\text { Line }} \\\ \text { } f(x)=\frac{1}{\sqrt{x-1}} \quad x+2 y+7\end{array}\)

Find the derivative of the algebraic function. \(f(x)=\left(x^{2}-x\right)\left(x^{2}+1\right)\left(x^{2}+x+1\right)\)

Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. $$ y=\frac{\cos \pi x+1}{x} $$