Answered: 26. f(x) = -: P(1, 1) %3D re) =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

find the slope of the line tangent to the
graph of ƒ at P.
b. Determine an equation of the tangent line at P

Expert Solution

Step 1

Given function:

$f (x) = \frac{1}{x}$

Step 2

To find the slope of the line tangent to the given function at P:

$Take the derivative of f (x) : \frac{d f (x)}{d x} = \frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x^{2}} And then, Find the value of - \frac{1}{x^{2}} for x = 1 : {\frac{d f (x)}{d x}}_{at x = 1} = - \frac{1}{1^{2}} = - 1 Therefore, Slope at point P = - 1$

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