This question: i point$($s$)$ posside

a$.$ Graph the function $f(x).$

b$.$ For what is $f^{\text{'}}(x)?$

c$.$ For $x>1,$ what is $f^{\text{'}}(x)?$

$f(x)=\{\begin{array}{ccc}-x& 1,& x1\\ -x& 3,& x>1\end{array}$

d$.$ Graph $f^{\text{'}}$ on its domain.

e$.$ Is f differentiable at $1?$ Explain.

d$.$ What is the graph of $f^{\text{'}}?$

A$.$ B$.$

c$.$ D$.$

d$.$ Is f differentiable at $1?$

A$.$ No$,f$ is not differentiable at $1$ because $f$ is not defined at $1.$

B$.$ No$,f$ is not differentiable at $1$ because $f$ has a cusp at $1.$

C$.$ No$,f$ is not differentiable at $1$ because $f$ is not continuous at $1.$

D$.$ No$,f$ is not differentiable at $1$ because $f^{\text{'}}(x)$ is different for $x<mn>1</mn>$ and $x>1.$

E$.$ No$,f$ is not differentiable at $1$ because $f$ has a vertical tangent at $1.$

F$.$ Yes, $f$ is differentiable at $1$ because $f^{\text{'}}(x)$ is the same for $x<mn>1</mn>$ and $x>1.$