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Use a linear approximation (or differentials) to estimate the given number.$ (1,999)^4 $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Adam D.

May 2, 2022

Okay but how do you get 2^4(1-4*.001/2)? Did you use linear approximation or differential?

Laura C.

October 15, 2021

awful explanation

Campbell University

Oregon State University

Baylor 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.

01:37

Use a linear approximation…

02:07

$23-28$ Use a linear appro…

02:41

02:03

00:27

02:18

Use an appropriate local l…

02:47

Okay, we know f of x is x to the fourth. Therefore, the change in x or delta x is negative. 0.001 point x is 2. Therefore, f of 2 minus 0.001 to the fourth power is 2 to the fourth times 1 minus 4 times 0.01 over 2, which is equivalent to 15.968.

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