Home
Class 12
MATHS
Let f be differentiable for all x. If f...

Let f be differentiable for all x. If `f(1)= -2, f'(x) ge 2` for all `x in [1, 6]`, then :

A

f(6) =5

B

`f(6) lt 5`

C

`f(6) lt 8`

D

`f(6) ge 8`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|200 Videos

Similar Questions

Explore conceptually related problems

Let f(x) satisfy the requirements of Largrange's Mean Value Theorem in [0, 2]. If f(0) = 0 and |f'(x)| le (1)/(2) , for all x in [0, 2], then :

Let f be a function defined for all x in R . If f is differentiable and f(x^(3)) = x^(5) for all x in R (x ne 0) , then the value of f^(')(27) is

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

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

Let f : R to R be a differentiable function and f(1) = 4 , then the value of lim_(x to 1) int_4^(f(x)) (2t)/(x - 1) dt is :

Let F : R to R be a differentiable function having : f(2) = 6, f'(2) = 1/48 Then lim_(x to 2) int_(6)^(f(x)) (4 t^3)/(x-2) dt equals :

Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then : lim_(x rarr 1) (f(1) g(x) - f(x) g(1) - f(1) + g(1))/(g(x) - f(x)) equals :

There exists a function f(x) satisfying f(0)=1, f'(0)=-1, f(x) gt 0 , for all x, then :

Let f(x) be a function satisfying f(x+y) = f(x) f(y) for all x,y in N such that f(1) = 3 and sum_(x=1)^(n) f(x) = 120 . Then the vlaue of n is :

HIMALAYA PUBLICATION-APPLICATION OF DIFFERENTIATION-QUESTION BANK
  1. A stone is thrown vertically upwards from the top of a tower 64 metres...

    Text Solution

    |

  2. The tangent to a given curve y=f(x) is perpendicular to the x -axis if

    Text Solution

    |

  3. A sphere increases its volume at the rate of picc//s. The rate at whic...

    Text Solution

    |

  4. The angle between y^(2)=4x and x^(2)+y^(2)=12 at a point of their inte...

    Text Solution

    |

  5. The slopes of the tangent and normal at (0, 1) for the curve y=sinx+e^...

    Text Solution

    |

  6. If for the curve y=1+bx-x^(2) the tangent at (1, -2) is parallel to x-...

    Text Solution

    |

  7. The surface area of a ball is increasing at the rate of 2 pi sq. cm/s...

    Text Solution

    |

  8. If the area of an expanding circular region increases at a constant ra...

    Text Solution

    |

  9. If f(x)=x^(alpha) logx and f(0)=0, then the value of alpha for which R...

    Text Solution

    |

  10. A point an the parabola y^(2)=18x at which the ordinate increases at t...

    Text Solution

    |

  11. If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a...

    Text Solution

    |

  12. Let f be differentiable for all x. If f(1)= -2, f'(x) ge 2 for all x ...

    Text Solution

    |

  13. If the equation a(n) x^(n) + a(n -1) x^(n-1) + .... + a(1) x = 0, a(1)...

    Text Solution

    |

  14. If a+b+c=0, then the equation 3ax^(2)+2bx+c=0 has :

    Text Solution

    |

  15. If f(x) satisfiles requirements of Rolle's theorem in [1,2] and f(x) i...

    Text Solution

    |

  16. Let f(x) = e^(x), x in [0,1], then a number c of the Lagrange's mean v...

    Text Solution

    |

  17. If f(x) satisfies of conditions of Rolle's theorem on [3,5], then int3...

    Text Solution

    |

  18. The function f(x) = x(x+3)e^(-x/2) satisfies all the conditions of Rol...

    Text Solution

    |

  19. In a triangle ABC if sides a and b remain constant such that alpha is ...

    Text Solution

    |

  20. The circumference of a circle is measured as 56 cm with an error 0.02 ...

    Text Solution

    |