Question

raph of $f(x)$ is shown below. estimate and list the value(s) of $x$ where $f(x)$ has a horizontal tangent.

Explanation:

Step1: Identify horizontal tangent meaning

A horizontal tangent to $f(x)$ occurs where the slope of the curve is 0, which corresponds to the local maxima and minima (the "peaks" and "valleys") of the graph.

Step2: Locate peaks/valleys on the graph

Looking at the given graph, the curve has a local minimum (valley) at $x = -3$ and a local maximum (peak) at $x = 3$. These are the points where the tangent line is horizontal.

Answer:

$x = -3$ and $x = 3$