AP Calc AB - Characteristics of Graphs

Concave Up: graph of f(x)

Concave Up: behavior of f''(x)

f"(x) is positive

Concave Up: behavior of f'(x)

f'(x) is increasing

Concave down: graph of f(x)

Concave down: behavior of f''(x)

f"(x) is negative

Concave down: behavior of f'(x)

f'(x) is decreasing

Critical values

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

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

f'(x) is negative

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

f'(x) is positive

Point of Inflection: behavior of f'(x)

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

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

f"(x) changes sign

Relative Maximum: behavior of f'(x)

f'(x) changes from positive to negative

Relative Maximum: behavior of f(x)

f(x) changes from increasing to decreasing

Relative Minimum: behavior of f'(x)

f'(x) changes from negative to positive

Relative Minimum: behavior of f(x)

f(x) changes from decreasing to increasing