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Let.$ f(x) = \left\{ \begin{array}{ll} x^2 + 1 & \mbox{if} x < 1\\ x + 1 & \mbox{if} x \ge 1 \\ \end{array} \right.$Is $ f $ differentiable at 1? Sketch the graphs of $ f $ and $ f '. $

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$f$ is not differentiable at 1

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

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.

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.

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Let$$f(x)=\left\{\…

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Let$$f(x)=\left\{\begi…

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Draw the graph of $f$; ind…

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Show that $f$ is not diffe…

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THINK ABOUT IT Sketch the …

Show that$$f(x)=\left\…

So it's the F differential poet. Well, I'll leave the sketching part of you. And for the first part, if it's not differentiable one bills derivative of this part is two X and this is two at X equals one. And the reality of this is what so which is one at ethics FC Host one and they do not match. Oh, when they don't match, you don't have a a value for the the slope of the tangent line, therefore is not differentiable.

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