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Draw a diagram to shoe that there are two tangent lines to the parabola $ y = x^2 $ that pass through the point (0, -4). Find the coordinates of the point where these tangent lines intersect the parabola.

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02:49

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Maya R.

March 2, 2022

Both explanations are awful, LAZY.

Oregon State University

Baylor University

Boston 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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Draw a diagram to show tha…

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Using a graph to help you,…

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Find the slope of the tang…

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Find an equation of the ta…

02:01

Hey, it's Claire. So when you read here So we're gonna note that all points of the problem Why equals X square or the form ex calmer X square in the 10 gin A comma a square pass History zero common negative floor We know that the slope of attention at any point is the derivative. So when we do a friend a tree we have two x So the slough off the tension at a comma A square iss to a And since this tension passes street of slope Hey, do the 0.8 common Any square and zero common negative four. We can write the slip detention as a square plus four over a which is equal to to a and then we get a is equal to positive or negative too. One of the tensions is to come before and the other is negative to Palmer for when we draw a graph, it looks like this men are tensions are gonna be in blue. This is Siro common negative for to karma four negative too common for

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