91Ó°ÊÓ

For the functions, a. sketch the graph and b. use the definition of a derivative to show that the function is not differentiable at \(x=1\). $$ f(x)=\left\\{\begin{array}{l} -x^{2}+2, x \leq 1 \\ x, x>1 \end{array}\right. $$

For the following functions, a. sketch the graph and b. use the definition of a derivative to show that the function is not differentiable at \(x=1.\) $$f(x)=\left\\{\begin{array}{l}{-x^{2}+2, x \leq 1} \\ {x, x>1}\end{array}\right.$$

For the functions, a. sketch the graph and b. use the definition of a derivative to show that the function is not differentiable at \(x=1\). $$ f(x)=\left\\{\begin{array}{l} 2 x, x \leq 1 \\ \frac{2}{x}, x>1 \end{array}\right. $$

For the following functions, a. sketch the graph and b. use the definition of a derivative to show that the function is not differentiable at \(x=1.\) $$f(x)=\left\\{\begin{array}{l}{2 x, x \leq 1} \\ {\frac{2}{x}, x>1}\end{array}\right.$$

Use \(f^{\prime \prime}(x)=\lim _{h \rightarrow 0} \frac{f^{\prime}(x+h)-f^{\prime}(x)}{h}\) to find \(f^{\prime \prime}(x)\). $$ f(x)=2-3 x $$

For the following functions, use \(f^{\prime \prime}(x)=\lim _{h \rightarrow 0} \frac{f^{\prime}(x+h)-f^{\prime}(x)}{h}\) to find \(f^{\prime \prime}(x).\) $$f(x)=2-3 x$$

Use \(f^{\prime \prime}(x)=\lim _{h \rightarrow 0} \frac{f^{\prime}(x+h)-f^{\prime}(x)}{h}\) to find \(f^{\prime \prime}(x)\). $$ f(x)=4 x^{2} $$

For the following functions, use \(f^{\prime \prime}(x)=\lim _{h \rightarrow 0} \frac{f^{\prime}(x+h)-f^{\prime}(x)}{h}\) to find \(f^{\prime \prime}(x).\) $$f(x)=4 x^{2}$$

For the following functions, use \(f^{\prime \prime}(x)=\lim _{h \rightarrow 0} \frac{f^{\prime}(x+h)-f^{\prime}(x)}{h}\) to find \(f^{\prime \prime}(x).\) $$f(x)=x+\frac{1}{x}$$

Use \(f^{\prime \prime}(x)=\lim _{h \rightarrow 0} \frac{f^{\prime}(x+h)-f^{\prime}(x)}{h}\) to find \(f^{\prime \prime}(x)\). $$ f(x)=x+\frac{1}{x} $$