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Where does the normal line to the parabola $ y = x^2 - 1 $ at the point (-1, 0) intersect the parabola a second time? Illustrate with a sketch.

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04:08

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

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.

44:57

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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Where does the normal line…

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Sketch a graph of the para…

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What point on the parabola…

Yeah, it's clear. So inhumane here. So we're finding where the normal line to the parappa below y equals X squared minus one. That negative one comma zero intersects the graph a second time. We're gonna first take the derivative and get two acts. And this gives us a slope of two. Which means our perpendicular slope is 1/2 which is our normal. So, are you normal? Up a M of end? We'll take the points, X I'm a X squared minus one and negative one comma zero. Get a square minus one minus zero. Over X minus. Negative one. We get excess ik X minus one. We're going to set them equal to each other for 1/2 is equal to X minus one. We get X is equal to three over two. You know why I value when we plug it in by over four. To get our normal line equation? We just put our X and why values in we get 1/2 X plus 1/2 the one we graft this. I look like this, our crapola. And then I lie. They touch each other, and right here we're talking about the intersection right here.

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