Dictionary

difference quotient en · NOUN

Meanings

1. A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations: ▸ The average rate of change of the function f(x) over the interval [a,,a+h]. As h approaches zero, the value of (f(a+h)-f(a))/h approaches the derivative or instantaneous rate of change of f(x) at x=a.
2. A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations: ▸ The slope of the secant line passing through the points (a,,f(a)) and (a+h,,f(a+h)). As the horizontal distance h>0 between the points approaches zero, the slope of this secant line approaches the slope of the tangent line to f(x) at x=a, which is equal to the derivative of f(x) at x=a.

Forms

Relateds

derivative · difference equation

Translations (14)

ca quocient de diferències (difference quotient) · it rapporto incrementale (difference quotient) · fr quotient des variations (difference quotient) · es cociente de diferencias (difference quotient) · es cociente incremental (difference quotient) · pt quociente de diferenças (difference quotient) · nl differentiaalquotiënt (difference quotient) · ast cociente diferencial (difference quotient) · de Differenzenquotient (difference quotient) · fr quotient des différences (difference quotient) · fi erotusosamäärä (difference quotient) · cmn 差商 (difference quotient) · da differenskvotient (difference quotient) · gl cociente da diferenza (difference quotient)