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8 Cards in this Set
- Front
- Back
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If f is decreasing on (a, b), then f ' (x) < 0 for each x in (a, b) |
False |
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If f and g are both decreasing on (a, b), then f − g is decreasing on (a, b).
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False |
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If f '(c) = 0, then f has a relative maximum or a relative minimum at x = c. |
False |
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If f(x) = ln(ax), then f '(x) = ln(a). |
True |
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If f(x) = eπ, then f '(x) = eπ. |
False. f(x) = eπ is a constant function and so f '(x) = 0. |
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If f ''(x) < 0 on (a, b) and f '(c) = 0 where a < c < b, then f(c) is the absolute maximum value of f on [a, b]. |
True. f ''(x) < 0 says that the graph is concave downward on (a, b). Therefore, the relative maximum value at x = c must, in fact, be the absolute maximum value. |
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If f is continuous on an open interval (a, b), then f does not have an absolute minimum value. |
False. Let f(x) = x2 on (−1, 1). |
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If the graph of f is concave upward on (a, c) and concave downward on (c, b), where a < c < b, then f has an inflection point at x = c. |
False. Let f(x) = − 1x.Then f is concave upward on (−∞, 0)and concave downward on (0, ∞), but f does not have an inflection point at 0. |
