second derivative
Rate of change's change
The second derivative is the derivative of a derivative—a measure of how the rate of change itself is changing.
In calculus, if the first derivative shows velocity (how position changes over time), the second derivative shows acceleration (how velocity changes).
A function's second derivative reveals whether its curve is concave up or concave down: The second derivative is positive, so the graph curves upward.
Inward-curving surface quality
- convexityOutward-curving quality
- inflection pointWhere curvature changes sign
- differentiationRecognizing meaningful differences
- chain ruleComposite function derivative method
product rule · notation · Leibniz · Newton · differential equation · antiderivative · tangent · slope
Directed rate of motion
- positionLocation or stance
- jerkAbrupt pulling motion
- kinematicsStudy of movement itself
- motionChange in position
displacement · time · free fall · projectile motion · deceleration · force · mass · momentum
Function's highest, lowest points
- minimaLowest possible quantities
- maximaGreatest possible values
- critical pointDecisive juncture in events
- saddle pointStationary point, not extremum
local maximum · local minimum · necessary condition · sufficient condition
concavity
Inward-curving surface quality
- convexityOutward-curving quality
- inflection pointWhere curvature changes sign
- differentiationRecognizing meaningful differences
chain rule · product rule · notation · Leibniz · Newton · differential equation · antiderivative · tangent · slope · rate of change
velocity
Directed rate of motion
- positionLocation or stance
- jerkAbrupt pulling motion
- kinematicsStudy of movement itself
motion · displacement · time · free fall · projectile motion · deceleration · force · mass · momentum · impulse
extrema
Function's highest, lowest points
- minimaLowest possible quantities
- maximaGreatest possible values
- critical pointDecisive juncture in events
saddle point · local maximum · local minimum · necessary condition · sufficient condition
bend
Curve or flex
second derivativeposition
Location or stance
antiderivative · integration · first derivative · velocity · integral
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