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Find the linearization $L(x)$ of the function at $a$.$f(x)=x^{3 / 4}, \quad a=16$

$L(x)=8+\frac{3}{8}(x-a)=8+\frac{3}{8} x-6=\frac{3}{8} x+2$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

00:57

Find the linearization $L(…

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01:26

$1-4$ Find the linearizati…

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Find the linearization $ L…

01:24

in this problem Where us? To find the lean years they showed up The function rac warrant. Uh, 16. So let's start with finding David. You're a primal backs from this is, um you were four extra native. What board and what's it like to function on their wits about at a given point of 16 is eight and F current 16 is for your egg. So the musician Opa have this F 16 plus eight prime 16 times X minus 16. So now we people look thanks and your eight 16 prime ships seen be finally musician to be three accelerate plus two

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