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

$$\left(-\frac{b}{2 a}, \frac{4 a c-b^{2}}{4 a}\right) \text { is a } \mathrm{m} \text { if } a > 0 \text { is a } \mathrm{M} \text { if } a < 0$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

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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.

01:01

Locate all critical points…

03:53

Classify all critical poin…

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03:04

02:55

02:28

Determine all critical poi…

01:12

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02:09

01:50

first we want to find the derivative of this equation and just keep in mind A. B and C. You're all constants. So we have using power world to A X plus B as our derivative, we want to find out what this equals zero. So solving for X, We get negative B over two. A. Is where X. Is Where X equals zero. So now that we have the location of our zero, we want to look at how it falls on our number line. So we got negative B was to eight. Now one critical point of information here is that this is a quadratic. So because we don't actually know the values of B or A, we can actually figure out um what is less than what is greater than it. But with this is the general formula for a quadratic. So we know it's either going to look like this or like this. So depending on that, we know that if A. Is negative, that means the quadriga is facing down, which means it will be a maximum point. And if A is positive, the quadratic will be facing up and will be a negative point. So we're going to plug this into X to get. I would say you can solve it out on your own just by plugging negative B over 28 into your ex, both in B. X and get squared and you get Y equals for a c minus B squared all over or A. So at this point negative B as our ex negatively over two ways or X value. And for a c minus B squared over forays are Y value. Depending if A is less than zero, then it's going to be a maximum and if A is greater than zero then it will be a minimum.

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