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Locate all critical points.$$f(x)=2 x^{4}+2 x^{3}-x^{2}-7$$

$$(-1,-8),(0,-7),(1 / 4,-899 / 128)$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Harvey Mudd College

University of Michigan - Ann Arbor

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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Locate all critical points…

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01:59

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Classify all critical poin…

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Find all critical points o…

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02:00

Determine all critical poi…

01:27

first let's reveal the definition of critical point. Any number in the do mine of the function at which derivative is zero or feels to exist is called the critical number. And if C is a critical number then the point c f c is called a critical point. So first we take the relative to this function. It's derivative F prime max as eight X cubed plus six X squared miners to X. And we can factor it into three parts. Great to to Eriks times for ads my nurse one times X plus one. And we let it echo zero. Then they have three solutions which ex echoes minus one at 00 or X equals one force. This we are the critical numbers and zero function value of these three points are minus eight minus seven and the miners 899 over 128 respectively. And hence we have three critical points which are minus one minus eight 07 Sorry. There were minor seven and one false miners 899 over 128.

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