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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

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Baylor University

Idaho State University

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.

04:34

Draw a diagram showing two…

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Draw a diagram to show tha…

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Tangent Lines Show that th…

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Show that any two tangent …

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Draw a diagram to shoe tha…

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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