Chapter 2.2, Problem 42E

$42.$

Match each observation $(a)-(e)$ with a conclusion $(A)-(E)$. Observations

The point $(3,4)$

is on the graph of $f\text{'}(x).$

The point $(3,4)$

is on the graph of $f(x).$

The point $(3,4)$

is on the graph of $f\text{'}\text{'}(x).$

The point $(3,0)$

is on the graph of $f\text{'}(x)$, and the point $(3,4)$

is on the graph of $f\text{'}\text{'}(x).$

The point $(3,0)$

is on the graph of $f(x)$, and the point $(3,-4)$

is on the graph of $f\text{'}\text{'}(x).$

Conclusions

$f(x)$

has a relative maximum point at $x=3.$

When $x=3,$ the graph of $f(x)$ is concave up.

When $x=3,$ the tangent line to the graph $y=f\left(x\right)$ has slope $4$.

When $x=3,$ the value of $f(x)$ is $4$.

$f(x)$ has a relative maximum point at $x=3.$