Question

the graph of f(x) is shown below. estimate and list the value of x where f(x) has a horizontal tangent. x = enter a list of integer or decimal numbers more... question help: video submit question jump to answer

Explanation:

Step1: Recall tangent property

A function $f(x)$ has a horizontal tangent where its derivative $f'(x)=0$, which corresponds to local maxima, minima or horizontal - plateau points on the graph.

Step2: Identify from graph

Looking at the graph, we can see that the function $f(x)$ has a local maximum around $x = - 4$ and a local minimum around $x=6$. At these points, the slope of the tangent line to the curve $y = f(x)$ is zero (horizontal tangent).

Answer:

$x=-4,6$