Question

question 1 - 1 point consider the graph of f(x) given below. at what value(s) of x does f(x) have a local minimum? if there are multiple values, separate them with a comma. if no minimum occurs, enter ∅ (found in the dropdown menu under the answer box by selecting the “sets” keyboard).

Explanation:

Step1: Recall local - minimum condition

A function \(y = f(x)\) has a local minimum at \(x = c\) when \(f^{\prime}(x)\) changes sign from negative to positive at \(x = c\).

Step2: Analyze the graph of \(f^{\prime}(x)\)

Examine the points where \(f^{\prime}(x)\) crosses the \(x\) - axis and changes sign from negative to positive.

Since the graph of \(f^{\prime}(x)\) is not provided in the text, we cannot give a numerical answer. But the general procedure is as above. If we had the graph of \(f^{\prime}(x)\), we would identify the \(x\) - values where \(f^{\prime}(x)\) goes from negative (below the \(x\) - axis) to positive (above the \(x\) - axis).

Answer:

Cannot be determined without the graph of \(f^{\prime}(x)\)