suppose f(x) is a continuous function with a continuous derivative, with domain -∞ < x < ∞. a portion of the…

suppose f(x) is a continuous function with a continuous derivative, with domain -∞ < x < ∞. a portion of the graph of y = f(x) is shown. remember this is the graph of y = f(x) and not the graph of y = f(x). for all of the following, enter the x - value where the extrema occurs, or dne if no such x - value exists. the following questions are about the derivative of f(x). based on the graph: the derivative of f(x) has a minimum value at x = the derivative of f(x) has a maximum value at x =

suppose f(x) is a continuous function with a continuous derivative, with domain -∞ < x < ∞. a portion of the graph of y = f(x) is shown. remember this is the graph of y = f(x) and not the graph of y = f(x). for all of the following, enter the x - value where the extrema occurs, or dne if no such x - value exists. the following questions are about the derivative of f(x). based on the graph: the derivative of f(x) has a minimum value at x = the derivative of f(x) has a maximum value at x =

Answer

Explanation:

Step1: Identify minimum of $y = f'(x)$

We look for the lowest - point on the graph of $y = f'(x)$. From the graph, the lowest point of $y = f'(x)$ occurs at $x = 5$.

Step2: Identify maximum of $y = f'(x)$

We look for the highest - point on the graph of $y = f'(x)$. Since the graph of $y = f'(x)$ shown does not have a highest point (it extends upwards without bound in the given domain), the maximum value of $y = f'(x)$ does not exist.

Answer:

The derivative of $f(x)$ has a minimum value at $x = 5$. The derivative of $f(x)$ has a maximum value at $x=\text{DNE}$.