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

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) ≥e^x, x ∈[0,1]` If the function `e^(-x)f(x)` assumes its min in the interval `[0,1]` at `x=1/4`, which of the following is true?

A

`f'(x)ltf(x),(1)/(4)ltxlt(3)/(4)`

B

`f'(x)gtf(x),0ltxlt(1)/(4)`

C

`f'(x)ltf(x),0ltxlt(1)/(4)`

D

`f'(x)ltf(x),(3)/(4)ltxlt1`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Differential Equations Exerise 7 :|1 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]rarrR 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 ?

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]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(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

Let f be a differentiable function satisfying the relation f(xy)=xf(y)+yf(x)−2xy .(where x, y >0) and f ′ (1)=3, then find f(x)

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

A function y=f(x) satisfies (x+1)f^(')(x)-2(x^(2)+x)f(x) = e^(x^(2))/(x+1), Aax gt -1 . If f(0)=5 , then f(x) is

Let f (x) be twice differentiable function such that f'' (x) lt 0 in [0,2]. Then :

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

    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 be a function. Suppose the function f is twice differ...

    Text Solution

    |

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

    Text Solution

    |

  6. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |

  7. Differentiate the following w.r.t x (log x)^(cos x)

    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: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  10. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

    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 t...

    Text Solution

    |

  14. At present, a firm is manufacturing 2000 items. It is estimated tha...

    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

    |