Question

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the graph of ( y = f ( x ) ) is shown below.
list the critical values of ( f ( x ) ):
enter the list of these values separated by commas.
question help: video

Explanation:

Step1: Recall the definition of critical values

Critical values of a function \(y = f(x)\) are the \(x -\)values where \(f^{\prime}(x)=0\) (horizontal tangent) or \(f^{\prime}(x)\) does not exist.

Step2: Analyze the graph

On the graph of \(y = f(x)\), the points where the slope of the tangent line is zero (local maxima or minima) or the graph has a “corner” (where the derivative does not exist in the traditional sense). Looking at the given graph, we identify the \(x -\)coordinates of these points.

Answer:

\(-2,-1,2,4,5\)