Home
Class 12
MATHS
f: [0.4]-> R is a differentiable functio...

`f: [0.4]-> R` is a differentiable function. Then prove that for some `a,bin(0,4)`, `f^2(4)-f^2(0)=8f'(a)*f(b)`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part II|22 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

f:[0.4]rarr R is a differentiable function.Then prove that for some a,b in(0,4)f^(2)(4)-f^(2)(0)=8f'(a)*f(b)

Let f:[0,4]rarr R be a differentiable function then for some alpha,beta in (0,2)int_(0)^(4)f(t)dt

Given a function f:[0,4]toR is differentiable ,then prove that for some alpha,beta epsilon(0,2), int_(0)^(4)f(t)dt=2alphaf(alpha^(2))+2betaf(beta^(2)) .

Let f is a differentiable function such that f'(x)=f(x)+int_(0)^(2)f(x)dx,f(0)=(4-e^(2))/(3) find f(x)

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

For all twice differentiable functions f : R to R , with f(0) = f(1) = f'(0) = 0

Let f is a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx, f(0) = (4-e^(2))/(3) , find f(x).

Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) = If g(x)=(f(2f^(2)(x)+2))^(2), then g'(0) equals

RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

    Text Solution

    |

  2. f: [0.4]-> R is a differentiable function. Then prove that for some a,...

    Text Solution

    |

  3. if all the function f(x)=a^2x^3-a/9x^2-2x-b arepositive and the minimu...

    Text Solution

    |

  4. if f(x) = {underset(a^(2) -2+ (sin (x-K))/(x-K))(3+|x-k|)," "underse...

    Text Solution

    |

  5. The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...

    Text Solution

    |

  6. Let f(x) =sin ({x})/(a) + cos ({x})/(a) where a gt 0 and {.} denotes t...

    Text Solution

    |

  7. Consider the equation x^4+4x^3-8x^2+K=0. Answer the following (1) Th...

    Text Solution

    |

  8. A function f(x) having the following properties, (i) f(x) is conti...

    Text Solution

    |

  9. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

    Text Solution

    |

  10. If y=(a x+b)/((x-1)(x-4)) has a turning value at (2,\ -1) find a\ &...

    Text Solution

    |

  11. if A be the area of a triangle, prove that the error in A resulting fr...

    Text Solution

    |

  12. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

    Text Solution

    |

  13. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

    Text Solution

    |

  14. find the interval of increasing and decreasing for the function g...

    Text Solution

    |

  15. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  16. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  17. For any acute angled DeltaABC find the maximum value of (sin A)/(A) +(...

    Text Solution

    |

  18. For what real values of a' and 'b' all the extrema of the function f(x...

    Text Solution

    |

  19. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

    Text Solution

    |

  20. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |