Question

Find an equation of the tangent line to the curve at the given point. $$ y=\frac{x+2}{x-3}, \quad(2,-4) $$

Name: Problem 7, Chapter 2: Calculus: Early Transcendentals, Metric Edition
Uploaded: 2022-09-11T12:14:36-08:00
Channel: Amelia Hardy
Description: Find an equation of the tangent line to the curve at the given point. y=(x+2)/(x-3), (2,-4)

   Find an equation of the tangent line to the curve at the given point.
$$
y=\frac{x+2}{x-3}, \quad(2,-4)
$$

Calculus: Early Transcendentals, Metric Edition

James Stewart,… 9th Edition

Chapter 2, Problem 7

Instant Answer

Solved by Expert Amelia Hardy

09/11/2022

Step 1

We use the quotient rule which states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. So, the Show more…

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Find an equation of the tangent line to the curve at the given point. $$ y=\frac{x+2}{x-3}, \quad(2,-4) $$

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Key Concepts

Derivative

The derivative of a function measures its instantaneous rate of change at any given point and provides the slope of the tangent line to the curve. This concept is central in calculus for understanding how functions behave and change.

Tangent Line

A tangent line is a straight line that touches a curve at a single point and has the same slope as the curve at that point. This line serves as the best linear approximation of the function near the point of tangency.

Quotient Rule

The quotient rule is a formula used to differentiate functions that are expressed as the ratio of two differentiable functions. It allows one to find the derivative of such rational functions accurately.

Point-Slope Form

The point-slope form is a method for writing the equation of a line when a point on the line and its slope are known. It is particularly useful in problems where the tangent line must be determined from the given function and point.

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