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If $ c > \frac {1}{2}, $ how many lines through t…

03:43

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Problem 84 Hard Difficulty

Draw a diagram showing two perpendicular lines that intersect on the y-axis and are both tangent to the parabola $ y = x^2. $ Where do these lines intersect?


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03:34

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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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.

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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

Problem 1
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Problem 6
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Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
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
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Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
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Problem 78
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Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

Hey, it's clear. So when you read here, so we have why is equal to X square? This is even a function symmetric around the white access, and we know that are perpendicular lines will have slopes of one and negative one, and they'll go through the y axis. So for the tangent slope of one for why is equal to X square, you have our derivative, which is equal to two X. You cook in one, and we get X is equal to 1/2. We find the white corn in it and it becomes 1/4. We're you know that it's even so have symmetry. So the other is gonna be negative 1/2 and one for we're gonna find the equation With the first slope of one. I get why minus why one is equal to m times X minus X one, and we get why minus 1/4 is equal to one times X minus 1/2 and this becomes a lie is equal to X minus 1/4 for negative one. We're going to do the same thing, and we get why is equal to negative X minus 1/4. We see where the lines intersect by making them equal to one another. When we see that it's Pax is equal to zero under why value becomes negative. 1/4 Put zero comma. Negative. 1/4. We're gonna draw next. Why? Looks like this then. Our tangents. What? This is negative. 1/2 and 1/4 This this positive 1/2 and 1/4 room. This is Hero Common negative 1/4.

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

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Caleb Elmore

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Michael Jacobsen

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Calculus 1 / AB Courses

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

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.

Join Course
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