Final answer:
The linearization of a function at a point is the equation of the tangent line to the graph of the function at that point. It can be found using the formula: L(x) = f(a) + f'(a)(x - a).
Step-by-step explanation:
The linearization of a function at a point refers to the equation of the tangent line to the graph of the function at that point. To find the linearization of a function, we use the formula:
L(x) = f(a) + f'(a)(x - a)
where L(x) is the linearization, f(a) is the value of the function at the point a, and f'(a) is the derivative of the function at the point a.
For example, if we have a function f(x) = 2x^2 - 3x + 1 and we want to find the linearization at a = 0, we can use the formula:
L(x) = f(0) + f'(0)(x - 0)
To find the coefficients for f(0) and f'(0), we substitute 0 into the function and its derivative:
L(x) = 1 + (-3)(x)
So the linearization of f(x) at a = 0 is L(x) = 1 - 3x.