/*! 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 55 Describe the \(x\) -values at wh... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 55

Describe the \(x\) -values at which the function is differentiable. Explain your reasoning. $$ y=\sqrt{x-1} $$

Short Answer

Expert verified
The function \(y=\sqrt{x-1}\) is differentiable for all \(x\) such that \(x\geq1\).

Step by step solution

01

Understand the given function

Given a function \(y=\sqrt{x-1}\) which is a standard square root function. A square root function in general is defined and differentiable for all values where the expression under the square root is non-negative. In this case, the expression under the square root is \(x-1\).
02

Define the domain of the function

The value under the square root should be greater than or equal to 0. That is, \(x-1\geq0\). If we solve for \(x\) we get \(x\geq1\). So the function is defined for all \(x\) that are greater than or equal to 1. Beyond this point the function is continuous and hence differentiable.
03

Conclusion

The function \(y=\sqrt{x-1}\) is differentiable for all \(x\) such that \(x\geq1\).

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

Use the General Power Rule to find the derivative of the function. $$ f(x)=\left(x^{2}-9\right)^{2 / 3} $$

Find an equation of the tangent line to the graph of \(f\) at the point \((2, f(2)) .\) Use a graphing utility to check your result by graphing the original function and the tangent line in the same viewing window. $$ f(x)=x \sqrt{x^{2}+5} $$

Use the General Power Rule to find the derivative of the function. $$ y=\sqrt[3]{9 x^{2}+4} $$

Use the General Power Rule to find the derivative of the function. $$ y=\sqrt[3]{3 x^{3}+4 x} $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ f(x)=x^{3}(x-4)^{2} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.