Q. 21 - Calculus

Question

In Exercises 21–24, sketch the graph of a function f that has the listed characteristics.

$$\begin{gathered} f\left(1\right)=2; \\ f\text{'}\left(1\right)=0; \\ f\text{'}\left(3\right)=2 \end{gathered}$$

Step-by-Step Solution

Answer

The graph of the function with the given characteristics is:

Step 1. Given Information.

The characteristics of the function:

$$\begin{gathered} f\left(1\right)=2; \\ f\text{'}\left(1\right)=0; \\ f\text{'}\left(3\right)=2 \end{gathered}$$

Step 2. Observe from the given information.

From the given information we can conclude that the function has a bend at $x=1$ since $f\text{'}\left(1\right)=0$.

And $f\left(1\right)=2$ so the function is a positive quantity at $x=2$

And the slope of the tangent $x=3$ is positive since it is $2$.

Step 3. Graph the function.

Graph the function.