Questions: Determine all x-values for which the graph of f has a horizontal tangent line on the closed interval [-9,9].

Determine all x-values for which the graph of f has a horizontal tangent line on the closed interval [-9,9].
Transcript text: Determine all $x$-values for which the graph of $f$ has a horizontal tangent line on the closed interval $[-9,9]$.
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Solution

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Solution Steps

Step 1: Identify potential x-values for horizontal tangents

Horizontal tangent lines occur where the slope of the function is zero, corresponding to local maximums and minimums on the graph. Visually inspect the graph to find these points.

Step 2: Locate x-values of maximums and minimums

The graph shows a local maximum around x = -3 and a local minimum around x = 1. There also appears to be a local maximum around x = 4.

Final Answer

x ≈ -3, 1, 4

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