Problem

What is the shortest possible length of the line …

04:55

Problem 56 Hard Difficulty

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

Name: at which points on the curve y 1 40x3 3x5 does the tangent line have the largest slope
Uploaded: 2021-02-10
Duration: 2 min 41 s
Channel: Numerade
Description: At which points on the curve $ y = 1 + 40x^3 - 3x^5 $ does the tangent line have the largest slope?

Answer

Slope is maximum at $(2,225)$ and $(-2,-233)$

Catherine R.

Missouri State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

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Video Transcript

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.

Linda H.

Oklahoma State University

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 7

Optimization Problems