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Find the linear approximation of the function $ g(x) = \sqrt [3]{1 + x} $ at $ a = 0 $ and use it to approximate the numbers $ \sqrt [3]{0.95} $ and $ \sqrt [3]{1.1}. $ Illustrate by graphing $ g $ and the tangent line.

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Nottingham

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.

03:27

Find the linear approximat…

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Find the linearization $L(…

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06:00

05:44

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01:51

Find the tangent line appr…

Okay, Jim zero is the cube root of one plus zero, which is one therefore, G prime of acts is 1/3 times. Now we're playing in zero. So one plus zero to the negative to over three simplifies to 1/3 plug into the blender or ization formula with sequels one plus 1/3 axe. So now we have one plus X equals 0.95 they're for ox equals negative 0.5 Therefore, we have one plus 1/3 times negative 0.5 0.9833 You know The cube root of 1.11 plus X is 1.1 an ax 0.11 plus 1/3 time's Your 0.1 is one point 1.3 three.

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