91Ó°ÊÓ

For the following exercises, find \(f^{\prime}(x)\) for each function. $$f(x)=\frac{x^{2}+4}{x^{2}-4}$$

For the following exercises, find \(f^{\prime}(x)\) for each function. $$f(x)=\frac{x+9}{x^{2}-7 x+1}$$

Find \(f^{\prime}(x)\) for each function. $$ f(x)=\frac{x+9}{x^{2}-7 x+1} $$

For the following exercises, find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$[\mathrm{T}] \mathrm{y}=3 x^{2}+4 x+1\( at \)(0,1)$$

Find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$ y=3 x^{2}+4 x+1 \text { at }(0,1) $$

For the following exercises, find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$[\mathrm{T}] \mathrm{y}=2 \sqrt{x}+1 at (4,5)$$

Find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$ y=2 \sqrt{x}+1 \text { at }(4,5) $$

For the following exercises, find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$[\mathrm{T}] \mathrm{y}=\frac{2 x}{x-1} at (-1,1)$$

Find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$ y=\frac{2 x}{x-1} \text { at }(-1,1) $$

For the following exercises, find the equation of the tangent line \(T(x)\) to the graph of the given function at the indicated point. Use a graphing calculator to graph the function and the tangent line. $$[\mathrm{T}] y =\frac{2}{x}-\frac{3}{x^{2}} at (1,-1)$$