Home
Class 12
MATHS
Draw a graph of the function y=[x]+|1-x|...

Draw a graph of the function `y=[x]+|1-x|,-1lexle3`. Determine the points if any where this function is not differentiable.

A

`(-1,0,1,2,3)`

B

`(-1,0,2)`

C

`(0,1,2,3)`

D

`(-1,0,1,2)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`f(x)={{:(,-x,-1 lexlt0),(,1-x,0lexlt1),(,x,1lexlt2),(,1+x,2lexlt3),(,5,x=3):}`
Clearly, f(x) is discontinuous at x=0,1,2 and 3.
So, it is not differentiable at these points.
At x=-1, we have
`underset(x to 1^(+))lim f(x)=underset(x to 1^(+))lim-x=1=f(-1)`
So, it is continuous at x=-1
Also, (RHD at x=1)=-1 (a finite number).
Therefore, f(x) is differentiable at x=-1
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|143 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of the function y=[x] in -2ltxlt4

Draw the graph of the function f(x)=|x-1|

Draw the graph of the function y=|x-2|+|x-3|

Draw the graph of the function y=|x-2|+|x-3|

Draw the graph of the function f(x)=-x|x| .

Draw the graph of function. y=|4-x^(2)|,-3lexle3 .

Draw the graph of the function f(x)=x^(x)

Draw the graph of function y = |2-|x-2|| .

Draw the graph of the function: f(x)=log|x|

Draw the graph of function. y=(1)/(|x|)

OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Draw a graph of the function y=[x]+|1-x|,-1lexle3. Determine the point...

    Text Solution

    |

  2. The function f(x) = (4-x^(2))/(4x-x^(3)) is discontinuous at

    Text Solution

    |

  3. Let f(x)=|x| and g(x)=|x^3| , then (a).f(x) and g(x) both are continuo...

    Text Solution

    |

  4. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

    Text Solution

    |

  5. The set of points where the function f(x)=x|x| is differentiable is...

    Text Solution

    |

  6. On the interval I = [-2, 2], if the function f(x) = {{:((x+1)e^(-((1)/...

    Text Solution

    |

  7. If f(x)={{:(,(|x+2|)/(tan^(-1)(x+2)),x ne -2),(,2, x=-2):}, then f(x) ...

    Text Solution

    |

  8. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

    Text Solution

    |

  9. The set of all points where the function f(x)=sqrt(1-e^(-x^2)) is di...

    Text Solution

    |

  10. The function f(x)=e^(-|x|) is continuous everywhere but not differe...

    Text Solution

    |

  11. The function f(x)=[cos x] is

    Text Solution

    |

  12. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

    Text Solution

    |

  13. If f(x) = sin ^(-1)((2x)/(1 + x^(2))) then f (x) is differentiable in ...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then f...

    Text Solution

    |

  16. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

    Text Solution

    |

  17. If f(x)= | log10x| then at x=1.

    Text Solution

    |

  18. If f(x)=|log(e) x|,then

    Text Solution

    |

  19. If f(x)=|log(e)|x||," then "f'(x) equals

    Text Solution

    |

  20. Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1a x^2+b\ \ \ \ \ \ \ \ for\ |x|...

    Text Solution

    |

  21. Let h(x)="min "{x,x^(2)} for every real number of x. Then, which one o...

    Text Solution

    |