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At what numbers is the following function $ g $ differentiable?$ g(x) = \left\{ \begin{array}{ll} 2x & \mbox{if}x \le 0\\ 2x - x^2 & \mbox{if}0 < x < 2\\ 2 - x & \mbox{if}x \ge 2 \end{array} \right. $Give a formula for $ g' $ and sketch the graphs of $ g $ and $ g'. $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

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.

03:45

At what numbers is the fol…

04:00

02:36

Find numbers $a$ and $b$ s…

06:56

Find all values of $x$ for…

00:29

X-Describe the x-Value…

14:08

Let$$f(x)=\left\{\begi…

01:03

Let$$ f(x)=\left\{\beg…

07:28

Let

$$f(x)=\left\{…

0:00

Graph and identify all $x$…

01:07

Find the value of $a$ that…

01:13

04:36

(a) Sketch the graph of th…

When is it differentiable the only possible points, it would not be differentiable. Is that those those boundary points? So we just have the check if they're derivative match at those boundary points. So let's take the derivative, which should be straight very straight forward, and this 1 should be minus 1 point so here when x equals 0. This 1 is 2. This 1 is 2 point. So at this point the sites to match match at x equals 0 and these 2 you probably x, equals 2. You have negative 2 and negative 1 so that they do not match at x. Equals 2 point. So the only point not differentiable is x equals 2. So g is differentiable for all x except x, equals 2 point and that leave the graphing part to you.

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