Applications of Derivatives · Applied Problems
Linearization
The linearization of f at a is the tangent line, used as a linear approximation of f near a. This is the same as the first-degree Taylor polynomial.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
Approximate √4.1 using linearization of f(x) = √x at a = 4.
- f(4) = 2, f'(x) = 1/(2√x), f'(4) = 1/4
- L(x) = 2 + (1/4)(x - 4)
- L(4.1) = 2 + (1/4)(0.1) = 2.025
Answer: √4.1 ≈ 2.025 (actual: 2.02485...)
1 more worked examplePremium
Approximate ∛8.06 using linearization of f(x) = x^(1/3) at a = 8.
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