Home
Class 12
MATHS
Prove that the greatest integer function...

Prove that the greatest integer function defined by`f(x) =[x] ,0 lt x lt 2` is not differentiable at `x=1`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • QUESTION BANK 2021

    CBSE MODEL PAPER|Exercise QUESTIONS|9 Videos

  • SAMPLE PAPER 2022

    CBSE MODEL PAPER|Exercise SECTION – C |10 Videos

Similar Questions

Explore conceptually related problems

Prove that the greatest integer function defined by f(x)=[x],0

Show that the function f(x)={:{(3+x", " xge0),(3-x", " x lt 0):} is not differentiable at x=0

Knowledge Check

  • Consider the greatest integer function, defined by f(x) =[x],0 le x lt 2 . Then,

    A
    f is derivable at x = 1
    B
    f is not derivable at x = 1
    C
    f is derivable at x = 1
    D
    None of the above

  • Consider the greatest integer function, defined by f (x ) = [x ], 0 lt= x lt= 2. Then,

    A
    f is derivable at x = 1
    B
    f is not derivable at x = 1
    C
    f is derivable at x = 2
    D
    None of these

  • Let f(x) ={{:( [x],-2le xle -(1)/(2) ),( 2x^(2)-1,-(1)/(2)lt xle2):}and g(x) =f(|x|)+|f(x)|, where [.] represents the greatest integer function . the number of point where |f(x)| is non - differentiable is

    A
    3
    B
    4
    C
    2
    D
    5

    • Similar Questions

    Explore conceptually related problems

    Show that the function f(x)={:{(x^2+2", " xge1),(2x+1", " x lt 1 ):} is always differentiable at x=1

    A function f defined as f(x)=x[x] for -1lexle3 where [x] defines the greatest integer lex is

    Let f(x) ={{:( [x],-2le xle -(1)/(2) ),( 2x^(2)-1,-(1)/(2)lt xle2):}and g(x) =f(|x|)+|f(x)|, where [.] represents the greatest integer function . the number of point where g(x) is non - differentiable is

    The primitive of the function f(x)=(2x+1)|sin x| , when pi lt x lt 2 pi is

    The values of a and b such that the function f defined as f(x)={{:(ax^(2)-b",",,|x|lt1),(-1//|x|",",,|x|ge1):} is differentiable are

    Home
    Profile