Linearization
Definition
Linearization is an approximation method used to estimate values of functions near a particular point by using their tangent lines.
Analogy
Think of linearization as using a ruler to draw a straight line that closely follows the shape of a curvy graph. Just like how we can estimate distances between points on paper with this straight ruler, linearization helps us estimate values of functions near specific points on their graphs.
Related terms
Taylor Series: A Taylor series is an expansion of a function into an infinite sum of terms, which allows for more accurate approximations than linearization alone.
Local Maximum/Minimum: These are points on a graph where nearby values are either greater (maximum) or smaller (minimum) than those around them.
Differentiability: A function is differentiable if it has derivatives defined for all points in its domain.
"Linearization" appears in:
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Practice Questions (6)
What is the main idea behind linearization in calculus?
What is the role of the derivative in linearization?
How can linearization be used to estimate the value of a function at a point?
What is the key assumption made when using linearization to approximate a function?
What is the purpose of linearization in real-world applications of calculus?
How does linearization relate to the concept of tangent lines?
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