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Find an equation of the tangent line to the curve at the given point.

$ y = x^3 - 3x + 1 $, $ (2, 3) $

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04:51

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Campbell University

University of Nottingham

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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Find an equation of the ta…

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So here we give an example of specific cubic function, let's say it has this sort of a shape and were given information that we're interested in the tangent line at the point. Let's call the point here 2:03. So the tangent line would be why I minus the value of the function at a certain point. So why minus Y. Of two would be equivalent to the derivative of the function at the X value times x minus The certain x value or interest in which the X -2. So this will give the equation of the tangent line. So we have function Y equals execute minus three X plus one. And if we take the derivative of this this would be equivalent to three X squared minus three. If we evaluate the derivative at the point X equals two, So be four times maybe four times 3, 12, 12 -3 is nine. So we'll be getting information. This would be rewriting this would be AY -3 Equals nine times x -2. And this means that Y equals nine x minus 18 plus three, which B nine x minus 15. And this is our final answer.

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