How to linearize a function?
Understand the Problem
The question is asking for the methods or steps required to linearize a function, which typically involves approximating a nonlinear function by a linear function around a point. This can include using concepts such as derivatives and Taylor series expansions.
Answer
L(x) = f(a) + f'(a)(x − a)
The final answer is L(x) = f(a) + f'(a)(x − a)
Answer for screen readers
The final answer is L(x) = f(a) + f'(a)(x − a)
More Information
Linearization is useful for approximating the value of a function near a given point using its tangent line.
Tips
A common mistake is forgetting to calculate either f(a) or f'(a) properly. Ensure both calculations are correct before applying the linearization formula.
Sources
- The web page with info on - CK-12 Foundation - flexbooks.ck12.org
- Display14-4-3 - University of Texas - web.ma.utexas.edu
- MAT131Online - Stony Brook University - math.stonybrook.edu
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