Home
Class 12
MATHS
If the function f:[0,4]vecR is different...

If the function `f:[0,4]vecR` is differentiable, the show that for `a , b , in (0,4),f^2(4))-(f^2(0))=8f^(prime)(a)f(b)`

A

`8 f'(a) . f(b)`

B

`4f(b). f(a)`

C

`2f'(b). f(a)`

D

`f(b). f(a)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Level -1|102 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

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

Let f:[2,7]vec[0,oo) be a continuous and differentiable function. Then show that (f(7)-f(2))((f(7))^2+(f(2))^2+f(2)f(7))/3=5f^2(c)f^(prime)(c), where c in [2,7]dot

Let f:[2,7]vec[0,oo) be a continuous and differentiable function. Then show that (f(7)-f(2))((f(7))^2+(f(2))^2+f(2)f(7))/3=5f^2(c)f^(prime)(c), where c in [2,7]dot

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

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

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

If f is a continuous function on [0,1], differentiable in (0, 1) such that f(1)=0, then there exists some c in (0,1) such that cf^(prime)(c)-f(c)=0 cf^(prime)(c)+cf(c)=0 f^(prime)(c)-cf(c)=0 cf^(prime)(c)+f(c)=0

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -2
  1. f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...

    Text Solution

    |

  2. f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...

    Text Solution

    |

  3. f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log(e)x). ...

    Text Solution

    |

  4. Given a function f:[0,4]toR is differentiable ,then prove that for som...

    Text Solution

    |

  5. With the help of Lagrange's formula, prove that (a-b)/(a) le log (a/b)...

    Text Solution

    |

  6. The function f(x)=int(0)^(x)sqrt(1-t^(4)) dt is such that

    Text Solution

    |

  7. The function (sin(x+a))/(sin(x+b)) has no maxima or minima if

    Text Solution

    |

  8. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

    Text Solution

    |

  9. If f(x) is a cubic polynomial which has local maximum at x=-1,If f(2...

    Text Solution

    |

  10. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

    Text Solution

    |

  11. The maximum value of the function f(x)=3x^(3)-18x^(2)+27x-40 on the s...

    Text Solution

    |

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

    Text Solution

    |

  13. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

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

    Text Solution

    |

  15. If the function f:[0,4]vecR is differentiable, the show that for a , b...

    Text Solution

    |

  16. For a twice differentiable function f(x),g(x) is defined as g(x)=f^(pr...

    Text Solution

    |

  17. A function y=f(x) has a second-order derivative f''(x)=6(x-1)dot It it...

    Text Solution

    |

  18. Function f(x), g(x) are defined on [-1, 3] and f''(x) > 0, g''(x) > 0 ...

    Text Solution

    |

  19. If a << b << c << d and x in R then the least value of the function,...

    Text Solution

    |

  20. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

    Text Solution

    |