/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 64 Use a graphing utility to find t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 64

Use a graphing utility to find the \(x\) -values at which \(f\) is differentiable. \(f(x)=\frac{2 x}{x-1}\)

Short Answer

Expert verified
The function \(f(x) = \frac{2x}{x-1}\) is not differentiable at \(x = 1\).

Step by step solution

01

Evaluating the given function

We are given the function \(f(x) = \frac{2x}{x - 1}\). The function is not defined when the denominator is zero because division by zero is undefined in mathematics. In this case, it's when \(x = 1\). Therefore, \(x = 1\) is a point of non-differentiability.
02

Exploring function graphically

Using the graphing utility, the function is plot for a range of \(x\) values. It will be observed that the graph of the function has a vertical asymptote at \(x = 1\). This implies that the function tends to 卤鈭� as \(x\) approaches 1 from the right or left respectively.
03

Finding points where the function is not differentiable

The function is not differentiable where it's undefined or at the points where the function has sharp turns or cusps. For this function, there is no value of \(x\) resulting in sharp turns or cusps, but \(x = 1\) is a point where the graph shows a vertical asymptote. So, it is the point of non-differentiability.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\( \text { Radway Design } \) Cars on a certain roadway travel on a circular arc of radius \(r\). In order not to rely on friction alone to overcome the centrifugal force, the road is banked at an angle of magnitude \(\theta\) from the horizontal (see figure). The banking angle must satisfy the equation \(r g \tan \theta=v^{2},\) where \(v\) is the velocity of the cars and \(g=32\) feet per second per second is the acceleration due to gravity. Find the relationship between the related rates \(d v / d t\) and \(d \theta / d t\)

Consider the equation \(x^{4}=4\left(4 x^{2}-y^{2}\right)\). (a) Use a graphing utility to graph the equation. (b) Find and graph the four tangent lines to the curve for \(y=3\). (c) Find the exact coordinates of the point of intersection of the two tangent lines in the first quadrant.

Find the derivative of the function. \(f(t)=t^{3 / 2} \log _{2} \sqrt{t+1}\)

Find the derivative of the function. \(h(\theta)=2^{-\theta} \cos \pi \theta\)

In Exercises \(81-88\), (a) find an equation of the tangent line to the graph of \(f\) at the indicated point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of a graphing utility to confirm your results. \(\frac{\text { Function }}{y=2 \tan ^{3} x} \quad \frac{\text { Point }}{\left(\frac{\pi}{4}, 2\right)}\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.