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Fidn an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same scree.$ y = 3x^2 - x^3, (1,2) $

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00:58

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

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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Fidn an equation of the ta…

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Find an equation of the ta…

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Find an equation for the t…

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Hey, it's Claire. So when you married here. So we have. Why is equal to three X square minus X cubed? We're gonna find the derivative. Do you lie over DX? This is equal to D six X minus three X square when we plug in one to get three. Why minus two is equal to three X minus one point slope form. We get three X minus one or our tangent line. So here we have our crab. Why, thanks. And we're gonna first graph aren't 100 line. So at Cerro, it's gonna be negative one. And at one, it's gonna be two. So this is art. Ancient line, then Original has Ah, it crosses the origin. It has a 0.24 goes above here and goes back down. So look something like this.

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