Home
Class 12
MATHS
Let f,[2,7]rarr[0,oo) be a continuous an...

Let `f,[2,7]rarr[0,oo)` be a continuous and differentiable function, Then the value if `(f(7)-f(2))((f(7))^2+(f(2))^2+f(2)xf(7))/3` is (where `cin(2,7)`)

A

`3f^2(c),f(c)`

B

`5f^2(c),f(c)`

C

`2f^2(c),f(c)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Let f:Rto R be a twice continuously differentiable function such that f(0)=f(1)=f'(0)=0 . Then

Let f(x) be a twice-differentiable function and f"(0)=2. The evaluate: lim_(x->0)(2f(x)-3f(2x)+f(4x))/(x^2)

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

If f(x) is differentiable and strictly increasing function, then the value of lim_(xto0)(f(x^2)-f(x))/(f(x)-f(0)) is

Let f(x) be a differentiable function and f'(4)=5 . Then lim_(x to 2) (f(4) -f(x^(2)))/(x-2) equals

Let f[-2,2]rarrR be a continuous function such that f(x) assumes only irrational values. If f(sqrt2)=sqrt2 ,

Let f be twice differentiable function satisfying f(1) = 1, f(2) = 4, f(3) =9 then :

Let f(x) be a differentiable function and f'(4)=5 . Then lim_(xrarr2)(f(4)-f(x^2))/(x-2) equals

Let f:(0,oo)toRR be a differentiable function such that f'(x)=2-(f(x))/(x) for all x in(0,oo) and f(1)ne1 . Then-

Let f: RvecR be a continuous and differentiable function such that (f(x^2+1))^(sqrt(x))=5forAAx in (0,oo), then the value of (f((16+y^2)/(y^2)))^(4/(sqrt(y)))fore a c hy in (0,oo) is equal to 5 (b) 25 (c) 125 (d) 625

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If A(x1,y1) an B(x2,y2) be two points on the curve y=ax^2+bx+c then La...

    Text Solution

    |

  2. 0 < a < b < ( pi/2​) and f(a,b)= (tanb−tana)/b-a

    Text Solution

    |

  3. Let f,[2,7]rarr[0,oo) be a continuous and differentiable function, The...

    Text Solution

    |

  4. If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p))...

    Text Solution

    |

  5. If y=|cosx|+|sinx|,then(dy/dx)"at"x=(2pi)/3 is

    Text Solution

    |

  6. The differential coefficient of f(logex) with respect to x, where f(x)...

    Text Solution

    |

  7. If f(x) = cosx. cos2x. Cos4x. Cos8x.cos16x, then f '(pi/4) is :

    Text Solution

    |

  8. If f(x)=log|2x|,x!=0 then f'(x) is equal to

    Text Solution

    |

  9. The derivative of an odd function is always

    Text Solution

    |

  10. If y=1/(1+x+x^2+x^3), then value of (d^2y)/(dx^2)at x=0 is

    Text Solution

    |

  11. The function f(x)=(cosx+isinx)(cos3x+isin3x)...{cos(2n-1)x+isin(2n-1)x...

    Text Solution

    |

  12. If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

    Text Solution

    |

  13. If x^3y^9=(x+y)^k and x(dy)/(dx)=y then k =

    Text Solution

    |

  14. If y=log(3x+5) and (d^2y)/(dx^2)=A/(3x+5)^2 then A =

    Text Solution

    |

  15. Let f be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x^3phi(x) for...

    Text Solution

    |

  16. If y=cos^(-1)cos[2sin^(-1)(cosx)] then (dy)/dx=

    Text Solution

    |

  17. If x^2+y^2=t+1/t and x^4+y^4=t^2+1/t^2 then (dy)/(dx)=

    Text Solution

    |

  18. If x=sin^(-1)(3t-4t^3),y=cos^(-1)(8t^4-8t^2+1) then (dy)/(dx)=

    Text Solution

    |

  19. If f(x)=e^xg(2x),g(0)=4 and g'(0) = 2 then f'(0) is equal to

    Text Solution

    |

  20. Let f(x)=sinx,g(x)=x^2 and h(x) = log x. If F(x)=(h(f(g(x)))), then F'...

    Text Solution

    |