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Locate all critical points.$$g(x)=a x^{2}+b x+c$$

$$\left(-\frac{b}{2 a}, \frac{4 a c-b^{2}}{4 a}\right)$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Missouri State University

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University of Nottingham

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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Classify all critical poin…

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Locate all critical points…

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Determine all critical poi…

02:09

00:47

01:52

Find all critical points o…

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Find all the critical poin…

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02:08

Any number in the demining function at which the derivative is either zero or fields to exist is called a critical number. And if say, is a critical number, then the point C. F C is called a critical point for this exercise refers to tick the relative to this function, which is G primary X echoes to A X plus B. And they like the derivative echo zero. And then we got the critical number. Richards X equals miners B over two. A. And the function value at this point is miners B squared over full. A plastic enhance the point minors B over two. A miners B squared over for a pastie is a critical point.

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