AP Calc AB - Characteristics of Graphs

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Concave Up: graph of f(x)

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1

Concave Up: graph of f(x)

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2

Concave Up: behavior of f''(x)

f"(x) is positive

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3

Concave Up: behavior of f'(x)

f'(x) is increasing

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4

Concave down: graph of f(x)

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5

Concave down: behavior of f''(x)

f"(x) is negative

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6

Concave down: behavior of f'(x)

f'(x) is decreasing

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7

Critical values

f'(x) = 0; f'(x) = Undefined

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8

Intervals in which f(x) is decreasing: behavior of f'(x)

f'(x) is negative

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9

Intervals in which f(x) is increasing: behavior of f'(x)

f'(x) is positive

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10

Point of Inflection: behavior of f'(x)

f'(x) is a relative minimum or relative maximum

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11

Point of Inflection: behavior of f''(x)

f"(x) changes sign

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12

Relative Maximum: behavior of f'(x)

f'(x) changes from positive to negative

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13

Relative Maximum: behavior of f(x)

f(x) changes from increasing to decreasing

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14

Relative Minimum: behavior of f'(x)

f'(x) changes from negative to positive

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15

Relative Minimum: behavior of f(x)

f(x) changes from decreasing to increasing

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