AP Calc AB - Characteristics of Graphs
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15 Terms
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Concave Up: graph of f(x)
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Concave Up: behavior of f''(x)
f"(x) is positive
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Concave Up: behavior of f'(x)
f'(x) is increasing
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Concave down: graph of f(x)
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Concave down: behavior of f''(x)
f"(x) is negative
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Concave down: behavior of f'(x)
f'(x) is decreasing
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Critical values
f'(x) = 0; f'(x) = Undefined
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Intervals in which f(x) is decreasing: behavior of f'(x)
f'(x) is negative
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Intervals in which f(x) is increasing: behavior of f'(x)
f'(x) is positive
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Point of Inflection: behavior of f'(x)
f'(x) is a relative minimum or relative maximum
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Point of Inflection: behavior of f''(x)
f"(x) changes sign
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Relative Maximum: behavior of f'(x)
f'(x) changes from positive to negative
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Relative Maximum: behavior of f(x)
f(x) changes from increasing to decreasing
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Relative Minimum: behavior of f'(x)
f'(x) changes from negative to positive
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Relative Minimum: behavior of f(x)
f(x) changes from decreasing to increasing