Home
Class 12
MATHS
Examine the continuity and differentiabi...

Examine the continuity and differentiability of the function `f(x)=3x+|x-1|"at "x=1`

Text Solution

Verified by Experts

The correct Answer is:
Continuous but not differentiable at x = 1.
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Mutiple Correct Answers Type )|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Integer Answer Type)|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( Very Short Answer Type Questions)|6 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

Similar Questions

Explore conceptually related problems

Examine the continuity and differentiability of the function f(x)=|sinx|atx=0 .

Examine the continuity and differentiability of f (x) =2x^(2)+1 " at "x=1 .

Test the continuity and differentiability of the function f(x)=|(x+1/2)[x]| by drawing the graph of the function when -2lt=x<2, where [dot] represents the greatest integer function.

Examine the differentiability of the function f(x)=|cosx| at x=(pi)/(2) .

f(x)={{:(5x-4,"when "0ltxle1),(4x^(2)-3x,"when "xgt1):} Discuss the continuity and differentiability of f(x)"at" x =1

Examine the differentiability of the function f(x)=|sinx-cosx| at x=(pi)/(4) .

Examine the continuity of the function f(x)= 2x^(2)-1" at "x=3 .

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Given {:(f(x)=x^(2)-2x+3," ""when "xlt1),(=2," ""when "x=1),(=2x^(2)-5x+5," ""when "x gt1):} Examine the differentiability of the function at x = 1 .

Examine the differentiability of f(x) =2x+|x-1| at x = 1