Solve the problem.
-Find the table that matches the graph below.

A) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & 0 \ \hline c & \frac{1}{4} \end{array}$
B) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline \mathrm{a} & 0 \ \hline \mathrm{b} & 0 \ \hline \mathrm{c} & \frac{7}{4} \end{array}$
C) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & \text { does not exist } \ \hline c & \frac{7}{4} \end{array}$
D) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & 0 \ \hline b & 0 \ \hline c & \frac{1}{4} \end{array}$

Question

Solve the problem.
-Find the table that matches the graph below.

A) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & 0 \ \hline c & \frac{1}{4} \end{array}$ 
B) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline \mathrm{a} & 0 \ \hline \mathrm{b} & 0 \ \hline \mathrm{c} & \frac{7}{4} \end{array}$ 
C) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & \text { does not exist } \ \hline b & \text { does not exist } \ \hline c & \frac{7}{4} \end{array}$ 
D) $\begin{array}{l|l} x & f^{\prime}(x) \ \hline a & 0 \ \hline b & 0 \ \hline c & \frac{1}{4} \end{array}$

Quizplus · Accepted Answer

From the graph, we can see that the slope of the tangent line at points $a$ and $b$ is $0$, while the slope at point $c$ is positive but less than $1$. Therefore, the only option that matches the graph is choice D, where $f'(a)=f'(b)=0$ and $f'(c)=\frac{1}{4}$.

Solve the Problem xf′(x)a does not exist b0c14\begin{array}{l|l}x & f^{\prime}(x) \\\hline a & \text { does not exist } \\\hline b & 0 \\\hline c & \frac{1}{4}\end{array}xabc​f′(x) does not exist 041​​​

Solve the Problem $\begin{array}{l|l}x & f^{\prime}(x) \\\hline a & \text { does not exist } \\\hline b & 0 \\\hline c & \frac{1}{4}\end{array}$