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Explain the concept of linearization and why we use this. I get that linearization is the...

Explain the concept of linearization and why we use this.

I get that linearization is the equation of the tangent line. But why is this relevant to estimating values?

Math   Calculus   
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Linearization is an effective method for approximating the output of a function y=f(x) at any x=a based on the value and slope of the function at x=b, given that f(x) is differentiable on [a,b] (or [b,a]) and that a is close to b. In short, linearization is a method of estimating the value of a function, f(x), near a point, x = a, using the following formula:

Linearization makes it possible to use tools for studying linear systems to analyze the behavior of a nonlinear function near a given point. The linearization of a function is the first order term of its Taylor expansion around the point of interest.

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