Solve the problem.
-Find the table that matches the given graph.
A) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & 0 \ \hline c & 1 \end{array}$
B) $\begin{array}{c|c} \mathrm{x} & \mathrm{f}^{\prime}(\mathrm{x}) \ \hline \mathrm{a} & 0 \ \hline \mathrm{b} & 0 \ \hline \mathrm{c} & -1 \end{array}$
C) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & 0 \ \hline c & -1 \end{array}$
D) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & \text { does not exist } \ \hline c & -1 \end{array}$

Question

Solve the problem.
-Find the table that matches the given graph. 
A) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & 0 \ \hline c & 1 \end{array}$ 
B) $\begin{array}{c|c} \mathrm{x} & \mathrm{f}^{\prime}(\mathrm{x}) \ \hline \mathrm{a} & 0 \ \hline \mathrm{b} & 0 \ \hline \mathrm{c} & -1 \end{array}$ 
C) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & 0 \ \hline c & -1 \end{array}$ 
D) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & \text { does not exist } \ \hline c & -1 \end{array}$

Quizplus · Accepted Answer

From the graph, we can see that at $x=a$, the function is not differentiable (sharp corner), so $f^\prime(a)$ does not exist. At $x=b$, the function has a horizontal tangent and hence $f^\prime(b)=0$. At $x=c$, the function has a negative slope and hence $f^\prime(c)<0$. The only table that matches this is option C.

Solve the Problem xf′(x)a does not exist b0c1\begin{array}{l|l}x & f^{\prime}(x) \\\hline a & \text { does not exist } \\\hline b & 0 \\\hline c & 1\end{array}xabc​f′(x) does not exist 01​​

Solve the Problem $\begin{array}{l|l}x & f^{\prime}(x) \\\hline a & \text { does not exist } \\\hline b & 0 \\\hline c & 1\end{array}$