뒤로Calculus Exam 2 Review – Extrema and Graph Analysis
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Q2. Does f(x) achieve a relative maximum when x = -4?
Background
Topic: Relative Extrema (Maximum/Minimum) from a Graph
This question tests your ability to identify relative maxima and minima by analyzing the graph of a function.
Key Terms:
Relative Maximum: A point where the function value is higher than at nearby points.
Relative Minimum: A point where the function value is lower than at nearby points.
Step-by-Step Guidance
Examine the graph at to see if the function value is higher than at points immediately to the left and right.
Check the slope of the curve near . If the curve changes from increasing to decreasing, this indicates a relative maximum.
Compare the function value at with nearby values to confirm if it is indeed a peak.
Consider whether the endpoint or open circle at affects the classification as a relative maximum.
Try solving on your own before revealing the answer!
Final Answer: False
At , the graph does not achieve a relative maximum. The function value at this point is not higher than at nearby points, and the curve does not change from increasing to decreasing.
