Differentials and Approximations - Theory & Concepts - Linear Approximation

Learn how to use differentials to approximate function values and calculate errors, and discover Newton's Method and Taylor/Maclaurin Polynomials.

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Linear Approximation: $f(x) = \sqrt{x}$

Base Point (

a

): 25

Change in

x

(

\Delta x

): 1.0

Target

x

26.0

Actual

f(x)

5.0990

Approx

L(x)

5.1000

Error0.0010

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Observation: The green dot is the base point $a$ . The closer $\Delta x$ is to $0$ , the closer the linear approximation $L(x)$ (red line) is to the actual function $f(x)$ (blue line).

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Linear Approximation: f(x)=xf(x) = \sqrt{x}f(x)=x​

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Linear Approximation: $f(x) = \sqrt{x}$