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# Instantaneous Rate of Change Calculator

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Instantaneous rate of change is defined as the rate of change of a particular point of time. For a function, the change in the function f(x) with respect to "x" value is known as rate of change. Instantaneous rate of change is same as slope of a line. This online instantaneous rate of change calculator calculates the rate of change at a particular point by finding the derivative of the function.

## Steps

Step 1 : Note down the given function with the given point in the problem.

Step 2 : Find the first derivative for a given time for a given function to get the instantaneous rate of change.

## Problems

Given below are the problems based on instantaneous rate of change.

### Solved Examples

Question 1: Find the instantaneous rate of change of the function  f(x) = $x^3 + 3x^2 + x − 2$ at x = 1 ?
Solution:

Step 1 : Given function : f(x) = $x^3 + 3x^2 + x − 2$

Step 2 :  First derivative of f'(x),
f'(x) = $3x^2 + 3(2x) + 1 − 0$
f'(x) = $3x^2 + 6x + 1$

At x = 1, the instantaneous rate of change is,
f'(1) = $3(1)^2 + 6(1) + 1 = 10$.

Therefore, the instantaneous rate of change at x = 1 is 10.

Question 2: Find the instantaneous rate of change for f(x) = 2$x^2$ - 9 at x = 2?
Solution:
Step 1 : Given function : f(x) = 2$x^2$ - 9

Step 2 :  First derivative of f'(x),
f'(x) = 4x - 0 = 4x
f'(x) = 4x

At x = 2, the instantaneous rate of change is,
f'(2) = 4(2) = 8.

Therefore, the instantaneous rate of change at x = 2 is 8.