Problem $3$ Let's say

the dotted graph is the graph of $f,$ and

the dashed graph is the graph of $g.$

One of the functions $f$ and $g$ is the derivative of the other one.

$($a$)$ Only one of these statements is true.

$f$ is the derivative of $g$

$g$ is the derivative of $f$

Make a big $T$ in the blank to indicate the true statement and abig $F$ in the blank to indicate the false statement.

$($b$)$ Explain how you can be absolutely sure that the false statement is false.