Multiple Choice
Determine where the local and absolute maxima and minima occur on the given graph of .
6. Graphical Applications of Derivatives
Intro to Extrema
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Determine where the local and absolute maxima and minima occur on the given graph of .
A
Absolute max of 4 at , Absolute min of at
B
Absolute max of 4 at , Local max of 4 at , No absolute or local mins
C
Absolute max of 4 at , Absolute min of 2 at
D
Absolute max of 4 at , Local max of 4 at , Local min of 2 at
Verified step by step guidance1
Step 1: Observe the graph of f(x) and identify the highest and lowest points. The graph reaches its highest value of 4 at x = -2, and this is the absolute maximum. The graph does not go higher than this value anywhere else.
Step 2: Determine if there are any local maxima. A local maximum occurs at x = -2, where the graph peaks at 4. This is also the absolute maximum.
Step 3: Check for absolute minima. The graph does not reach a global lowest point because it continues to decrease indefinitely as x approaches positive infinity. Therefore, there is no absolute minimum.
Step 4: Identify any local minima. A local minimum occurs at x = -5, where the graph dips to a value of 2 before increasing again.
Step 5: Summarize the findings: Absolute max of 4 at x = -2, Local max of 4 at x = -2, Local min of 2 at x = -5, and no absolute minimum.
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