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1. |
Locate the extrema for the graph of y = f(x). |
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A. |
The extrema are (-1, 1) and (4, 3). |
B. |
The extrema are (-2, 1) and (4, 3). |
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C. |
The extrema are (-2, 1),
(1, -1) and (4, 3). |
D. |
The extrema are (-2, 1) and (1, -1). |
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Hint |
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2. |
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. |
minimum |
B. |
point of inflection |
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C. |
maximum |
D. |
none is correct |
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Hint |
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3. |
Use a graphing calculator to graph g(x) = x3 - x + 1 and to determine and classify its extrema. |
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A. |
relative minimum:
(-0.6, 1.38);
relative maximum:
(0.6, 0.62) |
B. |
relative minimum:
(1.38, -0.6);
relative maximum:
(0.6, 0.62) |
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C. |
relative maximum:
(-0.6, 1.38);
relative minimum:
(0.6, 0.62) |
D. |
relative maximum:
(1.38, -0.6);
relative minimum
(0.6, 0.62) |
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Hint |
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4. |
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 absolute minimum of this function. |
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B. |
(3,4) is the point of inflection. |
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C. |
(3,4) is the absolute maximum of this function. |
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D. |
(3,4) is the relative maximum of this function. |
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Hint |
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5. |
The function f(x) = - (x + 2)3 - 3 has a critical point at x = -2. Determine whether this is the location of a maximum, minimum or a point of inflection. |
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A. |
minimum |
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B. |
point of inflection |
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C. |
maximum |
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D. |
extremum |
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Hint |
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