Home
Class 12
MATHS
Let f be a differentiable function on th...

Let f be a differentiable function on the open interval(a, b). Which of the following statements must be true? (i) f is continuous on the closed interval [a,b],(ii) f is bounded on the open interval (a,b)

A

Only I and II

B

Only I and III

C

Only II and III

D

Only III

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 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

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

Let f(x) be a differentiable function in the interval (0,2) then the value of int_(0)^(2)f(x) is

Let f(x) = (g(x))/(h(x)) , where g and h are continuous functions on the open interval (a, b). Which of the following statements is true for a lt x lt b ?

Let f be continuous on [a,b] and differentiable on (a,b). then,which of the following statements is FALSE?

Let f(x) be a differentiable function in the interval (0,2) , then the value of int_0^2 f(x) dx is :

Letfand g be differentiable on the interval I and let a, b in I,a lt b . Then

F is a continuous and differentiable function in the interval I which of the following is the complete set of possibilities where the function is strictly decreasing

Continuity in open interval and closed interval

A function f is defined on an interval [a, b]. Which of the following statement(s) is are incorrect? (A) If f(a) and f(b) have opposite signs,then there must be a point cin(a,b) such that f(c)=0.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  2. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  3. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  4. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  5. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  6. If the functions f : R -> R and g : R -> R are such that f(x) is conti...

    Text Solution

    |

  7. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  8. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  9. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |

  10. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  11. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

    Text Solution

    |

  12. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

    Text Solution

    |

  13. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  14. Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...

    Text Solution

    |

  15. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  16. Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...

    Text Solution

    |

  17. Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...

    Text Solution

    |

  18. Let f(x) be continuous and differentiable function for all reals and f...

    Text Solution

    |

  19. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

    Text Solution

    |

  20. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x ge -1),(sin(pi(x+a))",","for...

    Text Solution

    |