91Ó°ÊÓ

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line. \(f(x)=-3 x+4\) at \((-1,7)\)

Sketch the graph of the function \(f\) and evaluate \(\lim _{x \rightarrow a} f(x)\), if it exists, for the given value of \(a\). \(f(x)=\left\\{\begin{array}{ll}x-1 & \text { if } x \leq 3 \\ -2 x+8 & \text { if } x>3\end{array} \quad(a=3)\right.\)

Find the derivative of each function. \(f(x)=\frac{1}{\sqrt{2 x^{2}-1}}\)

Find the derivative of each function. \(y=\frac{1}{\left(4 x^{4}+x\right)^{3 / 2}}\)

Sketch the graph of the function \(f\) and evaluate \(\lim _{x \rightarrow a} f(x)\), if it exists, for the given value of \(a\). \(f(x)=\left\\{\begin{array}{ll}x & \text { if } x<1 \\ 0 & \text { if } x=1 \\\ -x+2 & \text { if } x>1\end{array} \quad(a=1)\right.\)

Find the derivative of each function. \(f(x)=\frac{1}{x^{2}+1}\)

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line. \(f(x)=3 x^{2}\) at \((1,3)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=-x^{3}+2 x^{2}-6\)

Find the derivative of each function. \(f(u)=\frac{u}{u^{2}+1}\)

Sketch the graph of the function \(f\) and evaluate \(\lim _{x \rightarrow a} f(x)\), if it exists, for the given value of \(a\). \(f(x)=\left\\{\begin{array}{ll}-2 x+4 & \text { if } x<1 \\ 4 & \text { if } x=1 \\ x^{2}+1 & \text { if } x>1\end{array} \quad(a=1)\right.\)