Home
Class 12
MATHS
Let f:[0,1]toR (the set of all real numb...

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^(2),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)

A

Both I and II are true

B

I is true and II is false

C

I is false and II is true

D

Both I and II are false

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|4 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

Let f[0, 1] -> R (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) leq e^x, x in [0, 1] .Which of the following is true for 0 lt x lt 1 ?

Let f:[0,1]rarrR (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) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ? (A) 0 lt f(x) lt oo (B) -1/2 lt f(x) lt 1/2 (C) -1/4 lt f(x) lt 1 (D) -oo lt f(x) lt 0

Let f:[0,1]rarrR (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) ge e^x, x in [0,1] If the function e^(-x)f(x) assumes its minimum in the interval [0,1] at x=1/4 , which of the following is true? (A) f\'(x) lt f(x), 1/4 lt x lt 3/4 (B) f\'(x) gt f(x), 0 ltxlt1/4 (C) f\'(x) lt f(x), 0 lt x lt 1/4 (D) f\'(x) lt f(x), 3/4 lt x lt 1

Let f :R to R be a function such that f(x) = x^3 + x^2 f' (0) + xf'' (2) , x in R Then f(1) equals:

For x in R-{1}, the function f(x) satisfies f(x)+2f((1)/(1-x))=x. Find f(2)

For all x in [1, 2] Let f"(x) of a non-constant function f(x) exist and satisfy |fprimeprime(x)|<=2. If f(1)=f(2), then (A) There exist some a in (1,2) such that f'(a)=0 (B) f(x) is strictly increasing in (1,2) (C) There exists atleast one c in (1,2) such that f'(c)>0 (D) |f'(x)| lt 2 AA x in [ 1,2]

Consider the function f(x) satisfyig the identity f(x)+f((x-1)/(x))=1+x,AA x in R-{0,1} and g(x)=2f(x)-x+1

ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  2. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

    Text Solution

    |

  3. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  4. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  5. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  6. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  7. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

    Text Solution

    |

  8. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  9. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |

  10. For the following question, choose the correct answer from the codes (...

    Text Solution

    |

  11. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

    Text Solution

    |

  12. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

    Text Solution

    |

  13. Let the population of rabbits surviving at a time t be governed by ...

    Text Solution

    |

  14. At present a firm is manufacturing 2000 items. It is estimated that th...

    Text Solution

    |

  15. The population p(t) at time t of a certain mouse species satisfies the...

    Text Solution

    |

  16. If (dy)/(dx)=y+3 and y(0)=2, then y(log2) is equal to

    Text Solution

    |

  17. Let I be the purchase value of an equipment and V(t) be the value afte...

    Text Solution

    |

  18. Solution of the differential equation cosxdy=y(sinx-y)dx, 0ltxlt(pi)...

    Text Solution

    |

  19. The differential equation which represents the family of curves y=c(1)...

    Text Solution

    |

  20. The differential equation of the family of circles with fixed radius ...

    Text Solution

    |