Question

the graph of the function f is shown below. which statement best describes the value of f(-7)?

Explanation:

Step1: Recall derivative meaning

The derivative $f'(-7)$ is the slope of the tangent line to the graph of $y = f(x)$ at $x=-7$.

Step2: Analyze graph at $x = - 7$

At $x=-7$, the function $y = f(x)$ is decreasing. A decreasing function has a negative - slope tangent line. Also, the graph appears to be relatively flat at $x = - 7$, so the magnitude of the slope is small.

Answer:

$f'(-7)$ is a small negative number.