Home
Class 12
MATHS
Given f'(1)=1and f(2x)=f(x)AAxgt0.If f'...

Given `f'(1)=1and f(2x)=f(x)AAxgt0.If f'(x)` is differentiable, then there exists a number `c in (2,4)` such that `f''(c )` equal

A

`-1//4`

B

`-1//8`

C

`1//4`

D

`1//8`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos
  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos
  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise For Session 6|4 Videos
  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos
  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Does there exist a point c(in)(0,pi/2) such that f' (c)= 0 where f(x) = sin 2x ?

Suppose f (x) is differentiable at x =1 and lim _( h to 0) (f (1 + h ))/(h) = 5. Then f'(1) equals :

If f(x)=(x-4)/(2sqrtx) , then f'(1) is equal to:

Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose the function f is twice differentiable,f(0)=f(1)=0 and satisfies f''(x)-2f'(x)+f(x)gee^(x),x in [0,1] Consider the statements. I. There exists some x in R such that, f(x)+2x=2(1+x^(2)) (II) There exists some x in R such that, 2f(x)+1=2x(1+x)

If f(x)=(x-4)/(2sqrt3) , then f'(1) is equal to?

Let f(x) = x(x-1)(x-2),x in [0,2]. Prove that 'f' satisfies the conditions of Rolle's Theorem and there is more than one 'c' in (0,2) such that f'(C ) = 0

If f(x) is continuous function in [0,2pi] and f(0)=f(2 pi ), then prove that there exists a point c in (0,pi) such that f(x)=f(x+pi).

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuous differentiable function with f'(x) !=0 and satisfies f(0)=1 and f'(0)=2 , then f(x)=e^(lambda x)+k , then lambda+k is equal to ..........

Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x in R, then f^(iv)(0) is equal

Given a real valued fuction f(x) which is monotonic and differentiable , prove that for any real number a and b, int_(a)^(b){f^(2)(x)-f^(2)(a)} dx = int_(f(a))^(f(b))2x{b-f^(-1)(x)} dx

ARIHANT MATHS-DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS -Exercise (Single Option Correct Type Questions)
  1. Let f(x)=|(1,1,1),(3x-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1,7x^(8)-1...

    Text Solution

    |

  2. The graphs y=2x^(3)-4x+2and y=x^(3)+2x-1 intersect in exactly 3 distin...

    Text Solution

    |

  3. In which of the following functions is Rolles theorem applicable? (a)f...

    Text Solution

    |

  4. The figure shows a right triangle with its hypotenuse OB along the y-a...

    Text Solution

    |

  5. Number of positive integral value(s) of a for which the curve y=a^(x) ...

    Text Solution

    |

  6. Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 h(x)={x},k(...

    Text Solution

    |

  7. If the function f(x)=x^(4)+bx^(2)+8x+1 has a horizontal tangent and a...

    Text Solution

    |

  8. Coffee is coming out from a conical filter, with height and diameter b...

    Text Solution

    |

  9. A horse runs along a circle with a speed of 20k m//h . A lantern is at...

    Text Solution

    |

  10. Water runs into an inverted conical tent at the rate of 20 ft^3/ min a...

    Text Solution

    |

  11. Let f(x)=x^3-3x^2+2x Find f'(x)

    Text Solution

    |

  12. The Curve possessing the property that the intercept made by the tange...

    Text Solution

    |

  13. If f(x) is continuous and differentible over [-2, 5] and -4lef'(x)le3 ...

    Text Solution

    |

  14. A curve is represented parametrically by the equations x=t+e^(at) and ...

    Text Solution

    |

  15. At any two points of the curve represented parametrically by x=a (2 co...

    Text Solution

    |

  16. Let F(x)=int(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)], then

    Text Solution

    |

  17. Given f'(1)=1and f(2x)=f(x)AAxgt0.If f'(x) is differentiable, then th...

    Text Solution

    |

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

    Text Solution

    |

  19. Let S be a square with sides of length x. If we approximate the change...

    Text Solution

    |

  20. Consider f(x)=int1^x(t+1/t)dt and g(x)=f'(x) If P is a point on the cu...

    Text Solution

    |