Home > Calculus > Instantaneous Rate of Change at a Point

What is the instantaneous rate of change formula?

Answer 1

Paisley Johnson

The derivative, which is defined as the instantaneous rate of change,

#lim_(Delta x ->0)(f(x+Deltax)-f(x))/(Delta x) #

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Answer 2

Christopher Agresta

The instantaneous rate of change of a function at a particular point is given by the derivative of the function with respect to the independent variable at that point. Mathematically, it is represented by the formula:

[ \text{Instantaneous rate of change} = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]

or equivalently,

[ \text{Instantaneous rate of change} = \frac{dy}{dx} ]

where (f(x)) is the function, (x) is the independent variable, and (y) is the dependent variable. This formula calculates the slope of the tangent line to the function's graph at the specified point, providing the rate at which the function is changing at that exact moment.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.