Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Determine the extrema on the given interval.$$f(x)=x^{4}-6 x^{3}+12 x^{2}+2 \text { on: }(a)[1,2] ;(b)[-1,2]$$

(a) $\mathrm{M}=18, \mathrm{m}=9$(b) $\mathrm{M}=18, \mathrm{m}=2$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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.

01:40

Determine the extrema on t…

01:07

Find the absolute extrema …

02:43

03:34

02:25

Locate the absolute extrem…

01:52

For each function:(a) …

02:44

05:30

a. Locate the critical poi…

02:09

00:58

01:55

first we want to find the critical point of this function. It take derivatives. If prime Mexico's for X cubed minus 12 X squared plus 12. Yeah. And then we put eggs in France. The second part is a quadratic function and start to echoes the square of nine miners four times two times true, it's negative. Hence it has no roots. So there's only one critical number which is X equals zero for part A. The interval is from 1 to 2 and the critical number is not visiting this interval and their values are nine and 18 has now is a meaningful and 18 Mexico for barbie. The interval is from minus 1 to 2 and zero is visiting the centrum. Then they evaluate the function values. So 20 Y is a maximum and two is a meaning.

View More Answers From This Book

Find Another Textbook

02:33

Find $d y / d x$ using any method.$$x^{2}-x y+7=0$$

03:43

If $x^{2}+y^{2}=169,$ find $d y / d t$ when $x=5$ and $d x / d t=-6$

01:49

Given the parabola, $y=x^{2} .$ (a) Find the slope of the line connecting th…

03:57

The volume of blood flowing through an artery whose radius is $r$ is proport…

05:24

Determine the equation of the tangent line to the given curve at the indicat…

03:33

Find $d y / d x$ at the indicated point in two different ways: (a) Solve for…

03:41

Determine the equations of the tangent lines from the point (0,13) to the cu…

02:15

Consider the function given by$$f(x)=\left\{\begin{aligned}-2 x+1 &a…

04:28

(a) $f(x)=\left(x^{2}+2\right)\left(x^{4}-7\right) .$ Find $d f.$(b) $y=…

01:04

The price of a magazine, in cents, is given by the equation $p=10(147-0.02 x…