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[5] [6] The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). [7] [8]: 237 [9] The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change. [9]
In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad ...
Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change , and the slopes of curves , while the latter concerns accumulation of quantities, and areas under or between curves.
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
Rate of change may refer to: Rate of change (mathematics) , either average rate of change or instantaneous rate of change Instantaneous rate of change , rate of change at a given instant in time
Jerk (also known as jolt) is the rate of change of an object's acceleration over time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s 3 ( SI units ) or standard gravities per second ( g 0 /s).
Calculus is a branch of mathematics, developed from algebra, trigonometry, and geometry. Calculus focuses on rates of change (within functions ), such as accelerations , curves , and slopes .