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f(x) has a rel max when
f’(x) changes from positive to negative
f(x) has a rel min when
f’(x) changes from negative to positive
F(x) is concave down when
F'‘(x) is negative
F(x) is CCU when
f'‘(x) is positive
F(x) has a point of inflection at
A relative extrema/changes from increasing to decreasing or vice versa on f’(x)
F(x) is increasing when
F'(x) is positive
F(x) is decreasing when
F’(x) is negative
F(x) is CCU when
F'(x) is increasing
F(x) is CCD when
F’(x) is decreasing
F(x) has a point of inflection when
F’’(x) changes signs
F’(x) is increasing when
F'‘(x) is positive