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Where is the function $ h(x) = \mid x - 1 \mid + \mid x + 2 \mid $ differentiable? Give a formula for $ h' $ and sketch the graph of $ h $ and $ h'. $

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01:43

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Oregon 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.

04:48

Where is the function $h(x…

02:40

"Let h(x) = x +kxl:

00:23

Graph the function.$$<…

00:58

Sketch the graph of functi…

00:18

00:56

sketch the graph of h(x)=1…

01:24

01:33

A function $h(x)$ is defin…

03:09

Sketch the graph of the fu…

01:07

01:11

Hey, it's clear. So when you read here so we have Agent X is equal to the absolute value of X minus one was the absolute value of X plus two is equal to negative X minus one minus X plus two. This is for X is less than or equal to negative, too. We have negative X minus one less X plus two, and this is for access between negative two and one. We have X minus one less X plus two. This is for X is larger than one. These equations can be rewritten and simplified. Negative two X minus one. This can be three, and this is two x plus one When we differentiate it, we had the following negative, too access less than or equal to negative, too. Zero for access between negative two and one and two for X is bigger than one. So we see that it's not continuous, but negative two and one so it does not exist. That X is equal to negative two and one. When we take the formula, we get the absolute value of X plus two over X plus two. What's the absolute value of X minus one what were X minus one? We're going to also draw a graph where reference When we get the original graph. Just a Jiff. X looks like this. And then we have our derivative grab in red.

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