Linearization is the idea of approximating a continuous function around a point with a line.
For a continuous function f(x), we linearize f(x) around point a as
f(x)≈f(a)+f′(a)(x−a).
More interesting things happen in higher dimensions:
f(x)≈f(a)+∂f(x)∂x1|a+∂f(x)∂x2|a+…
or
f(x)≈f(a)+∇f|a⋅(x−a).
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