Home
Class 12
MATHS
lff is a differentiable function satisfy...

lff is a differentiable function satisfying `f(1/n)=0,AA n>=1,n in I`, then

A

`f(x) = 0, x in (0, 1]`

B

`f'(0) = 0 = f(0)`

C

f(0) = 0 but f'(0) not necessarily zero

D

`|f(x)| le 1, x in (0, 1]`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|6 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) is a continuous and differentiable function and f((1)/(n))=0AA n>=I and n in I, then a) f(x)=0,x in(0,1] b) f(c)=0,f(0)=0 c),(0)=0=f(0),x in(0,1] d) f(0)=0 and f'(0) need not be zero

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

If f(x) is a differentiable function satisfying |f'(x)| le 2 AA x in [0, 4] and f(0)=0 , then

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =

If f(x) is continuous and differerntiable function such that f((1)/(n))=0 for all n in N , then

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

If f(x) is a differentiable real valued function satisfying f''(x)-3f'(x) gt 3 AA x ge 0 and f'(0)=-1, then f(x)+x AA x gt 0 is

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in[0,1] for which f'(c)(f(c))^(n-1)>sqrt(2^(n-1)), where n in N.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. For every pair of continuous functions f,g:[0,1]->R such that max{f(x)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |