Instantaneous Rate of Change Calculator

Rate of change is the change in the ‘y’ value with respect to the change in the ‘x’ value and can be easily calculated by finding the derivative of the given function. Instantaneous rate of change is the rate of change at a given particular ‘x’ value. Instantaneous rate of change calculator is the online tool which can instantly find the rate of change at the given point.

Example 1: Find the instantaneous rate of change of the function, f(x) = 2x² –9 at x=1.

Given function, f(x) = 2x² – 9

Here we first find the rate of change for the given function  Take the derivative of f(x).

Derivative, f’(x) = 4x - 0 = 4x

f’(x) = 4x

Now to find the instantaneous rate of change at x = 1, we find derivative value at x = 1.

f’ (1) = 4 * 1 = 4

Instantaneous rate of change at x = 1  4


 
Example 2: Find the instantaneous rate of change of the function, f(x) = 4x³ at x=2.

Given function, f(x) = 4x³

Here we first find the rate of change for the given function  Take the derivative of f(x).

Derivative, f’(x) = 4 * 3 * x²

f’(x) = 12x²

Now to find the instantaneous rate of change at x = 2, we find derivative value at x = 2.

f’ (2) = 12 * 2² = 48

Instantaneous rate of change at x = 2  48