Practice Step-by-step Method For Finding Maxima/minima (4)

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6 sample questions

Question 1.
What is a critical point?
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Think about where the slope of the tangent line is zero.
Question 2.
Define local maxima and minima in your own words.
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Consider how hills and valleys look on a graph.
3Question 3.
What is a critical point?
- Where f'(x) > 0
- Where f'(x) = 0 or is undefined
- Where f''(x) = 0
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Think about where the slope of the function changes.
4Question 4.
True or False: A local minimum occurs when the first derivative changes from negative to positive.
- True
- False
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Consider the sound of a valley on a graph.
Question 5.
A farmer wants to fence a rectangular area of 200 m². Determine the dimensions that would minimize the fencing needed.
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Set area = length * width and use the perimeter formula to create equations.
Question 6.
A box with a square base and an open top must have a volume of 500 cm³. Find the dimensions that minimize the material needed.
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Use volume constraints to express the height in terms of base area and apply derivatives.

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