Home
Class 11
MATHS
Let f be differentiable for all x , If f...

Let `f` be differentiable for all `x ,` If `f(1)=-2a n df^(prime)(x)geq2` for all `x in [1,6],` then find the range of values of `f(6)dot`

A

`f(6)=5`

B

`f(6)lt5`

C

`f(6)lt5`

D

`f(6)gt8`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|4 Videos
  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos
  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|19 Videos

Similar Questions

Explore conceptually related problems

Let f be differentiable for all x, If f(1)=-2 and f'(x)>=2 for all x in[1,6] then find the range of values of f(6)

If f (x) is continous on [0,2], differentiable in (0,2) f (0) =2, f(2)=8 and f '(x) le 3 for all x in (0,2), then find the value of f (1).

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

Let f be a function which is continuous and differentiable for all real x.If f(2)=-4 and f'(x)>=6 for all x in[2,4], then

Suppose that f is differentiable for all x and that f^(prime)(x)lt=2fora l lxdot If f(1)=2a n df(4)=8,t h e nf(2) has the value equal to 3 (b) 4 (c) 6 (d) 8

OBJECTIVE RD SHARMA-MEAN VALUE THEOREMS-Exercise
  1. If 2a+3b+6c=0, then prove that at least one root of the equation a x^2...

    Text Solution

    |

  2. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |

  3. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  4. If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...

    Text Solution

    |

  5. Let (a0)/(n+1)+(a1)/n+(a2)/(n-1)++(a(n-1))/2+an=0. Show that there e...

    Text Solution

    |

  6. The number of values of k for which the equation x^3-3x+k=0 has two di...

    Text Solution

    |

  7. Let f(x)=(x-4)(x-5)(x-6)(x-7) then. (A)fprime(x)=0 has four roots (B)T...

    Text Solution

    |

  8. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

    Text Solution

    |

  9. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  10. The equation x log x = 3-x has, in the interval (1,3) :

    Text Solution

    |

  11. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

    Text Solution

    |

  12. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

    Text Solution

    |

  13. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

    Text Solution

    |

  14. The value of c in Largrange's theorem for the function f(x)= log(e) s...

    Text Solution

    |

  15. n is a positive integer. If the value of c presecribed in Rolle's th...

    Text Solution

    |

  16. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

    Text Solution

    |

  17. The number of real root of the equation e^(x-1)+x-2=0, is

    Text Solution

    |

  18. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

    Text Solution

    |

  19. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

    Text Solution

    |

  20. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

    Text Solution

    |