Linear Approximation Calculator

Linear Approximation Calculator is a free online tool that displays the linear approximation for the given function. BYJU’S online linear approximation calculator tool makes the calculation faster, and it displays the linear approximation in a fraction of seconds.

How to Use the Linear Approximation Calculator?

The procedure to use the linear approximation calculator is as follows:
Step 1:Enter the function, variable and its expansion point in the respective input fields
Step 2: Now click the button “Find the Linear Approximation” to get the output
Step 3:Finally, the linear approximation for the given function will be displayed in the new window

What is Meant by Linear Approximation?

A linear approximation is a method of determining the value of the function f(x), nearer to the point x = a. This method is also known as the tangent line approximation. In other words, the linear approximation is the process of finding the line equation which should be the closet estimation for a function at the given value of x. The linear approximation formula for the function is given by:
f(x) ≈ L(x) = f(a) + f’(a)(x-a)

Example

Question:
Determine 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.
Solution:
We know that the linear approximation formula is
f(x) ≈ L(x) = f(a) + f’(a)(x-a)
Now, substitute the values in the formula, 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