Download the App!

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

Question

Answered step-by-step

At which points on the curve $ y = 1 + 40x^3 - 3x^5 $ does the tangent line have the largest slope?

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Linda Hand

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

03:52

Wen Zheng

01:30

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 7

Optimization Problems

Derivatives

Differentiation

Volume

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

0:00

At which points on the cur…

03:22

01:57

Where on the curve $y=\lef…

03:15

Where on the curve $y=\fra…

01:17

What is the smallest possi…

equals one plus 40 X cubed minus three X to the fifth. Does the tangent line have the largest? Look. Okay, so largest. We're gonna maximize something. Gonna maximize slope of the tangent line. All right? And to find the slope of the tangent line, we have to take the derivative. So m tan. Because why prime, which is 1 20 X square minus 15 x to the fourth. Okay, now, we're not gonna set that equal to zero because we're not looking for the tangent is equal to zero or looking for the maximum tangent. So we have to take the derivative of it in 10. Prime. So to 40 x minus 60 x cubed equals zero. We confected out of 60 x and we get four minus x squared. So X is plus or minus two. And so then why is one plus 40 times two cubed minus three times to to the fifth tomorrow. Plus too cute 40 minus 12 one. Plus, um, maybe why don't I just do this on my calculator? That might be easier. Okay, let's see now. You know what? I can do that to Cuba today. Eight times 43. 20 to do the 5th, 32 32 times 3 96. So 3. 21 minus 96 five two. So 2. 25. So two comma 2 25. And then if you put a minus in there, it's minus 3 28 plus 96. So it will be 3. 20 minus 97. So three forever tu minus 2 23 minus 2 a.m. minus 2. 23.

View More Answers From This Book

Find Another Textbook