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Locate all critical points.$$f(x)=x^{2}-2 x+3$$

$$(1,2)$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

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.

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Locate all critical points…

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Find all critical points o…

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Determine all critical poi…

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Classify all critical poin…

Any number in the mind of a function out of which the derivative is either zero or fields to exist is called a critical number. And if say, is a graphical number, then the partner c f C is called a critical point. So we first take the relative to this function is to regulate areas have prime, etc. Coz two x minus two. And we like the decorative equals zero and hence we get acts echoes one, which is a critical number, and F one he goes to and hence the points 12 is a critical point.

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