Let $u(x)=\{\begin{array}{ll}3x^2& x\le 4\\ 24x-48& x>4\end{array}$. Is $u$ differentiable at $x=4$?

Let $u(x)=\{\begin{array}{ll}-2x^2& x\le 1\\ -4x+2& x>1\end{array}$. Is $u$ differentiable at $x=1$?

Is $u(x)=\{\begin{array}{ll}{x}^2& x\le 3\\ 6x-15& x>3\end{array}$ differentiable at $x=3$, and why?

The figure shows the graph of $w$. Why does $w^{\prime }(-3)$ fail to exist?

At what value of $x$ is $f(x)=\sqrt[3]{x-3}$ not differentiable, and why?

The figure shows the graph of $p$. Why does $p^{\prime }(1)$ fail to exist?

At what value of $x$ is $f(x)=\sqrt[3]{x-2}$ not differentiable, and why?

Is $p(x)=\{\begin{array}{ll}3x^2& x\le -3\\ -18x-25& x>-3\end{array}$ differentiable at $x=-3$, and why?

At what value of $x$ is $f(x)=\left|7x-7\right|$ not differentiable, and why?

Let $p(x)=\{\begin{array}{ll}2x^2& x\le -2\\ -8x-8& x>-2\end{array}$. Is $p$ differentiable at $x=-2$?

At what value of $x$ is $f(x)={\left(x-5\right)}^{2/3}$ not differentiable, and why?

For a function $s$ that is CONTINUOUS at $x=-3$, the left-hand derivative limit at $x=-3$ is $-\infty$ and the right-hand one is $\infty$. Which describes the graph there?

The figure shows the graph of $q$. Why does $q^{\prime }(3)$ fail to exist?

Is $v(x)=\{\begin{array}{ll}4x^2& x\le -2\\ -16x-13& x>-2\end{array}$ differentiable at $x=-2$, and why?

The figure shows the graph of $r$. Why does $r^{\prime }(0)$ fail to exist?

At what value of $x$ is $f(x)=\sqrt[3]{x-7}$ not differentiable, and why?

For a function $p$ that is CONTINUOUS at $x=-5$, the left-hand derivative limit at $x=-5$ is $-\infty$ and the right-hand one is $\infty$. Which describes the graph there?

Let $g(x)=\{\begin{array}{ll}3x^2& x\le -3\\ -18x-27& x>-3\end{array}$. Is $g$ differentiable at $x=-3$?

For a function $q$ that is CONTINUOUS at $x=-5$, the left-hand derivative limit at $x=-5$ is $-2$ and the right-hand one is $3$. Which describes the graph there?

At what value of $x$ is $f(x)=\left|2x+2\right|$ not differentiable, and why?

Let $s(x)=\{\begin{array}{ll}3x^2& x\le -2\\ -12x-12& x>-2\end{array}$. Is $s$ differentiable at $x=-2$?

The figure shows the graph of $v$. Why does $v^{\prime }(3)$ fail to exist?

Is $q(x)=\{\begin{array}{ll}-3x^2& x\le 3\\ -18x+33& x>3\end{array}$ differentiable at $x=3$, and why?

The figure shows the graph of $f$. Why does $f^{\prime }(2)$ fail to exist?