← MATH 01130 · Calculus I
MATH 01130 · Applications of derivatives
Increasing/decreasing, concavity
Definition
f is increasing where f′>0, decreasing where f′<0. Concave up where f′′>0 (slope increasing); concave down where f′′<0. Inflection: concavity changes.
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Sign chart for f′ using critical points (f′=0 or undefined) finds increase/decrease intervals.
Sign chart for f′′ finds concavity and candidates for inflection (f′′=0 or undefined, then verify sign change).
First derivative test and second derivative test classify local extrema.
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1.For f(x)=x³−3x, find intervals of increase and inflection points.