Practice Maxima And Minima (optimization) (4)

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5 sample questions

Question 1.
Define the terms maxima and minima.
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Think about peaks and valleys.
Question 2.
State the first step to find critical points in a function.
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What happens to the slope of the function at these points?
3Question 3.
What is the significance of critical points in a function?
- Their derivatives are zero.
- They are where functions are defined.
- They are minimum points.
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Think about where the slope flattens.
4Question 4.
True or False: A negative second derivative implies a local maximum.
- True
- False
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Consider the curvature of the graph.
Question 5.
Using the function f(x) = x^4 - 8x^2 + 16, find all local maxima and minima, and classify them using both derivative tests.
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You need to apply both first and second derivative evaluations after finding critical points.

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