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Instantaneous Rate of Change Calculator
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At any particular point or any instant if we are interested in finding the rate of change it is called Instantaneous rate of change. The graph below represents the instantaneous rate of change at any given points. Instantaneous Rate of Change Calculator calculates the rate of change taking place at any particular point for a given function for any variable.

A function is given below as default input for this calculator. First derivative of the function is calculated and rate of change value is substituted to get the instantaneous rate of change on clicking "Find Instantaneous Rate of Change".

Steps for Instantaneous Rate of Change Calculator

Step 1 :

Read the problem and observe the given quantities

Step 2 :

Find the first derivative for the given function and also find the value of the variable for the given point to get the answer.

Problems on Instantaneous Rate of Change Calculator

1. Find the Instantaneous rate of change of the function f(x) = x + 9 at x = 3?

Step 1 :

Given Function is f(x) = x + 9.

Step 2 :

Find the first derivative of the function
f'(x) = 1 + 0
= 1
Since we have instantaneous rate of change at x = 3
f'(3) = 1.

The Instantaneous rate of change for function f(x) = x + 9 at x = 3 is 1.

2. Find the Instantaneous rate of change of the function f(x) = 3x2 + 5x + 9 at x = 4?

Step 1 :

Given Function is f(x) = 3x2 + 5x + 9.

Step 2 :

Find the first derivative of the function
f'(x) = 3(2x) + 5 + 0
= 6x + 5
Since we have instantaneous rate of change at x = 4
f'(4) = 6(4) + 5
= 29.