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Let $ f(x) = (x - 1)^2 g(x) = e^{-2x} $and $ h(x) = 1 + \ln(1 -2x) $(a) Find the linearization of $ f, g $ and $ h $ at $ a = 0. $ What do you notice? How do you explain what happened?(b) Graph $ f, g, $ and $ h $ and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

06:13

Let $\quad f(x)=(x-1)^{2} …

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$$ \begin{array}{ll}{\text…

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(a) Find the linear approx…

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Linear approximation and c…

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01:01

(a) If $f(x)=x^{3}-2 x+2,$…

02:44

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On a graph of $f(x)=x^{2}$…

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(a) find the specified lin…

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The linearization is the b…

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Linear approximation and t…

Okay. We know that because each part of X is native to over one plus two acts, you know h of zero is one, and hpe from zero is gonna be negative to. Therefore, we have one month's two acts. Recall the old three liberalizations are equivalent to each other because G prime of zero is the same as all the other variables. Promise here, As you can see, if X is greater than zero than F G and H go from best to worst. If X is less than zero after an edge or at h f G go from best to worst.

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