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Find equation of both lines that are tangent to the curve $ y = x^3 - 3x^2 + 3x - 3 $ and are parallel to the line $ 3x - y = 15. $

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01:47

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Harvey Mudd College

Baylor 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.

02:46

Find equations for two lin…

01:17

Find an equation of the ta…

09:52

Find equations of both lin…

01:35

02:29

Find all points on the cur…

it's clear. So when you married here you can write three X minus Y equals 15 as why is equal to three X minus 15. Then this is equal to em. You differentiate our function, we got Do I over DX is equal to three x square minus six x plus three. Three is equal to three X square minus six X plus three. When we get X, I'm X minus two is equal to zero. So X has to be equal to zero or two. When Xs equal to zero, we have a why Volume two So the tangent passes through zero common negative three. The equation of the tension is why equals three X minus three access equal to two. Then we have to calm a negative one. So the equation off the tangent becomes why is equal to three X minus seven.

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