Pregunta
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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 Schwartz Luna. in the United States
Mar 13,2025

Solución de inteligencia artificial de Upstudy

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To find the relative maxima and minima of the function \( f \), follow these steps: 1. **Identify Critical Points:** Look for points where the slope changes (where \( f'(x) = 0 \) or is undefined). 2. **Determine Maxima:** Find points where \( f(x) \) is higher than nearby points. 3. **Determine Minima:** Find points where \( f(x) \) is lower than nearby points. **Example Answers:** - **Relative Maxima:** If \( f \) has maxima at \( x = a \) and \( x = b \), write: - A. The function \( f \) has relative maxima at \( a, b \) (with corresponding maximum values \( f(a), f(b) \)). - **Relative Minima:** If \( f \) has minima at \( x = c \) and \( x = d \), write: - A. The function \( f \) has relative minima at \( c, d \) (with corresponding minimum values \( f(c), f(d) \)). If there are no maxima or minima, select the appropriate option accordingly.

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Beyond the Answer

To analyze the graph of the function \( f \), we look for points where the graph reaches peaks or valleys. Typically, relative maxima occur where the slope changes from positive to negative, while relative minima occur where the slope changes from negative to positive. To give you specific numbers or values, I would need to see the graph itself. However, you can find relative maxima by identifying local peaks and noting their coordinates (x-values). Similarly, look for local troughs to determine the relative minima. Happy graph hunting! Let those peaks and valleys guide you to the answers!

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