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Let$ f(x) = \left\{ \begin{array}{ll} x^2 + & \mbox{if} x \le 2\\ mx + b & \mbox{if} x > 2\\ \end{array} \right. $Find the values of $ m $ and $ b $ that make $ f $ differentiable everywhere.

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01:09

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Harvey Mudd College

University of Michigan - Ann Arbor

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.

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Let$$f(x)=\left\{\…

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It's close when you reign here, so for have to be differential everywhere. It has to be differential. X equals to us. Well, so the derivative one approaching from both sides of X equals two has to be equal to one another. Sorry. When we differentiate half a pecs is equal to two X and we get four. Well, we know that M X plus be is a line. So that means that the slope has to be equal to four since that day since the differentiated equation is equal to em for X, this bigger been too. And now we're going to find for be so f of two is equal to four if X is less than or equal to two. So we're gonna solve for B. Why is he equal to M X plus be? We plug in four equal to four times two plus B and we gotta be value of negative for

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