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At what point on the curve $ y = 1 + 2e^x - 3x $ …

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Problem 59 Medium Difficulty

Find equation of both lines that are tangent to the curve $ y = x^3 - 3x^2 + 3x - 3 $ and are parallel to the line $ 3x - y = 15. $


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01:47

Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

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Derivatives

Differentiation

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Top Calculus 1 / AB Educators
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Anna Marie Vagnozzi

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Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Watch More Solved Questions in Chapter 3

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Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
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Problem 25
Problem 26
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Problem 28
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Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
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Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
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Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

it's clear. So when you married here you can write three X minus Y equals 15 as why is equal to three X minus 15. Then this is equal to em. You differentiate our function, we got Do I over DX is equal to three x square minus six x plus three. Three is equal to three X square minus six X plus three. When we get X, I'm X minus two is equal to zero. So X has to be equal to zero or two. When Xs equal to zero, we have a why Volume two So the tangent passes through zero common negative three. The equation of the tension is why equals three X minus three access equal to two. Then we have to calm a negative one. So the equation off the tangent becomes why is equal to three X minus seven.

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Calculus: Early Transcendentals

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Related Topics

Derivatives

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

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Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

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Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

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In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
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