Home
Class 12
MATHS
If f(x) be such that f(x) = max (|3 - x|...

If f(x) be such that `f(x) = max (|3 - x|, 3 - x^(3))`, then

A

f(x) is continuous `AA x in R`

B

f(x) is differentiable `AA x in R`

C

f(x) is non-differentiable at three points only

D

f(x) is non-differentiable at four points only

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If "f(x)" be such that f(x)=max{|2-x|,2-x^(3)} ,then

If f(x) = |x+3|, then f'(3)=

If f(x)=x+(1)/(x) , such that f^3 (x)=f(x^(3))+lambdaf((1)/(x)) , then lambda=

If f ( x ) = |x - 3| , then f' ( 3 ) is

Let f be a function such that f(3)=1 and f(3x)=x+f(3x-3) for all x. Then find the value of f(300).

f(x)=max{tan x,cot x)

If f(x)=|x-3|, then f(3) equals

If f(x)=(3x+2)/(4x-3) show that f(x)=f^(-1)(x)

If f(x)=(1+x)/(1-x), show that: f(2x)=(3f(x)-1)/(3-f(x)) .

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x) be such that f(x) = max (|3 - x|, 3 - x^(3)), then

    Text Solution

    |

  2. For every pair of continuous functions f,g:[0,1]->R such that max{f(x)...

    Text Solution

    |

  3. Let f:R-> R and g:R-> R be respectively given by f(x) = |x| +1 and g...

    Text Solution

    |

  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

    Text Solution

    |

  5. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

    Text Solution

    |

  7. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

    Text Solution

    |

  8. For the fucntion f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. Let g(x) = ((x -1)^(n))/(log cos^(m)(x-1)),0 lt x lt 2, m and n are in...

    Text Solution

    |

  10. Let f and g be real valued functions defined on interval (-1, 1) such ...

    Text Solution

    |

  11. In the following, [x] denotes the greatest integer less than or equal ...

    Text Solution

    |

  12. If f(x)=min.(1,x^2,x^3), then

    Text Solution

    |

  13. Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/a...

    Text Solution

    |

  14. lff is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, t...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={t a n^(-1)x ,if|x|l...

    Text Solution

    |

  16. The left hand derivative of f(x)=[x]sin(pix) at x = k, k is an intege...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0? cos (|x|...

    Text Solution

    |

  18. For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)), then

    Text Solution

    |

  19. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |