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1. |
Locate the extrema for the graph of y = f(x). |
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A. |
The extrema are (-2, 1) and (4, 3). |
B. |
The extrema are (-2, 1), (1, -1) and (4, 3). |
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C. |
The extrema are (-2, 1) and (1, -1). |
D. |
The extrema are (-1, 1) and (4, 3). |
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Hint |
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2. |
Use the graphing calculator f(x) = x3 + x2 - x, and locate the relative maximum point. |
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A. |
There is no relative maximum point. |
B. |
(-1, 0.833) |
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C. |
(0.5, -0.292) |
D. |
(0, 0) |
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Hint |
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3. |
The function f(x) = 3x2 - x3 has critical points at x = 0 and x = 2. Determine whether each of these critical points is the location of a relative maximum, relative minimum, or a point of inflection. |
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A. |
(0, 0) minimum and (2, 4) point of inflection |
B. |
None of these is correct. |
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C. |
(0, 0) maximum and (2, 4) minimum |
D. |
(0, 0) minimum and (2, 4) maximum |
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Hint |
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4. |
Determine whether the given critical point of x = -7 is the location of a relative maximum, relative minimum, or a point of inflection for the function f(x) = x3 + x2 + 1. |
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A. |
maximum |
B. |
minimum |
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C. |
point of inflection |
D. |
none is correct |
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Hint |
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5. |
The function f(x) = -(x - 3)2 + 4 has a critical point at x = 3. Determine and classify this point. |
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A. |
(3,4) is the point of inflection. |
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B. |
(3,4) is the relative maximum of this function. |
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C. |
(3,4) is the absolute minimum of this function. |
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D. |
(3,4) is the absolute maximum of this function. |
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Hint |
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