Get better grades,
Forget about deadlines, with top 2% experts across the board. Your high school and college homework assignments are not your problem anymore.

What Is a Local Linear Approximation Calculator?

It is a free online tool that can derive the linear approximation formula for a given function and use it to calculate the approximate values. A linearization calculator incorporates some of the popular numerical techniques, such as Ranga Kutta methods and Euler’s Method. 


In the linearization of a function calculator, computations are on the proximity of the tangent line to the graph of the specified function around a particular point. You can use linear approximation to estimate solutions to ordinary differential equations.


Linearization Formula

Now, for us to find the multivariable linear approximation of a function f at a point x = a, we should have two things in mind:

  • m, which is the slope of the line
  • A single point that the line goes through, (a, b)

These two will give us the equation of the line.

  • y – b = m(x–a)

In such problems, the values of b or m will not be provided. That is where you have to use the linear approximation steps to find them. 

  • First, take m = f ‘(a), 
  • Then, b = f(a), 

When we collate all these to find the value of y using a linear approximation multivariable calculator, the formula will be as follows:

  • y – b = m(x–a)
  • y = b + m(x–a)
  • m(x–a)
  • y = f (a) + f `(a)(x-a)

With the formula, you can now estimate the value of a function, f(x), near a point, x = a.

How To Do Linear Approximation

The 3d linear approximation calculator or multivariable linear approximation calculator is used in many fields of science. You will have to incorporate a bit of calculus to find a derivative. Here is how to find linearization using the formula derived above:


Find the value of the f (3.5) using the linear approximation at a=2, whose function f(x) is differentiable such that f(3)= 12, and f’(3) = -2.


The linear approximation formula is

f(x) ≈ L(x) = f(a) + f’(a)(x-a)

When the values are substituted in the formula, here is what we get

L(x) = f(3) + f’(3)(x-3) = 18-2x

Hence, f(3.5)= 18-2(3.5)

f(3.5)= 18 – 7

f(3.5) = 11

But with the linear approximation calculator, you can arrive at the answer in a blink of an eye with the following steps.

How To Use The Linear Approximation Online Calculator

Follow the steps below to find your approximate values on our linear approximation calculator:

  • First, key in the function, variable and its expansion point in the input fields provided
  • Then click the “Find the Linear Approximation” button to find your answer
  • Lastly, the linear approximation for the given function will appear in a new window

Calculus or algebra doesn’t have to feel like rocket science anymore. 

Best Math Homework Helpers For You

If the calculator answers are not enough for you, we have the best helpers at hand - just write them "do my math homework for me"! Whether it’s linear approximation, calculus, algebra or deriving a function, our professional math gurus can help.

Let’s make your assignment go away.
Awesome. Now you'll never miss out.