Question

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 submit question

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 (corner, cusp, or vertical tangent).

Step2: Identify the points on the graph

Looking at the graph of \(y = f(x)\):

• At \(x=-5\), the function has a local maximum (horizontal tangent, \(f^{\prime}(x) = 0\)).
• At \(x=-2\), the function has a local minimum (horizontal tangent, \(f^{\prime}(x)=0\)).
• At \(x = 0\), the function has a local maximum (horizontal tangent, \(f^{\prime}(x)=0\)).
• At \(x=1\), the function has a local minimum (horizontal tangent, \(f^{\prime}(x)=0\)).

Answer:

\(-5,-2,0,1\)