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The graph of a function f is given. Use the graph to find each of the following. a. The numbers, if any, at which f has a relative maximum. What are these relative maxima? b. The numbers, if any, at which f has a relative minimum. What are these relative minima? a. Find the numbers, if any, at which f has a relative maximum, and find the relative maxima(maximum). Select the corre to complete your choice. A. The function \( f \) has (a) relative maxima(maximum) at (Use a comma to separate answers as needed.) B. The function f has no relative maxima. b. Find the numbers, if any, at which f has a relative minimum, and find the relative minima(minimum). Select the corre complete your choice.

Ask by Black Marshall. in the United States
Mar 13,2025

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To find the relative maxima and minima of the function \( f \), analyze the graph to identify points where the slope changes from positive to negative (relative maxima) or from negative to positive (relative minima). Record the \( x \)-coordinates and corresponding \( f(x) \) values for these points. If no such points exist, state that there are no relative maxima or minima.

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The Deep Dive

To properly address the extremes of a function, it helps to visualize and analyze the graph closely. A relative maximum occurs where the function's value is higher than the values immediately surrounding it. Similarly, a relative minimum is where the function dips below the values nearby. So, if you observe peaks on the graph, those are your relative maxima, and any valleys represent relative minima. When examining the graph, note the coordinates of the peaks and valleys to accurately identify where the function increases and decreases, guiding you to the exact points where these relative extremum values occur. Common mistakes include overlooking local maxima or minima that might not be the highest or lowest points on the entire graph.

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