Questions: Given the graph of the function above, which of the following would be the graph of the derivative function f'?

Transcript text: myopenmat Exam 2 (Chapter 3) Exam 2 (Chapter 3) 100 points possible Answered: $21 / 30$ Question 22 Given the graph of the function above, which of the following would be the graph of the derivative function $f^{\prime}$ ?

Solution

Solution Steps

Step 1: Identify Critical Points

Identify the points where the function has a horizontal tangent (i.e., where the derivative is zero). These are the points where the function changes direction, which occur at the local maxima and minima.

Step 2: Determine the Slope Behavior

Determine the behavior of the slope (derivative) between the critical points. If the function is increasing, the derivative is positive. If the function is decreasing, the derivative is negative.

Step 3: Sketch the Derivative

Using the information from the previous steps, sketch the graph of the derivative function. The derivative will be zero at the critical points, positive where the function is increasing, and negative where the function is decreasing.

Final Answer

The graph of the derivative function $ f' $ will have zeros at the x-values of the local maxima and minima of the original function. It will be positive where the original function is increasing and negative where the original function is decreasing.

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