Home
Class 12
MATHS
If f(x) and g(x) are differentiable func...

If f(x) and g(x) are differentiable functions for `0lexle1` such that f(0)=2,g(0)=0,f(1)=6,g(1)=2, then in the interval (0,1)

A

`f'(c)=g'(c)`

B

`f'(c)=2g'(c)`

C

`2f'(c)=g'(c)`

D

`2f'(c)=3g'(c)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f(x) and g(x) are differentiable function for 0lexle1 such that f(0)=2,g(0)=0,f(1)=6,g(1)=2 , then show that these exist c satisfying 0ltclt1andf'(c)=2g'(c)

Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such taht f^(prime)(c)=2g^(prime)(c)dot Then the value of g(1) must be 1 (b) 3 (c) -2 (d) -1

f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x)-g''(x)=0, f'(1)=2, g'(1)=4, f(2)=3 and g(2)=9 , then [f(x)-g(x)] at x=(3)/(2) is equal to -

If f and g are differentiable functions in [0, 1] satisfying f(0)=2=g(1),g(0)=0" and "f(1)=6 , then for some c in [0,1] -

Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0)=0,f(1)=6 and g(1)=2. Show that there exists c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot

If f(x) and g(x) are twice differentiable functions on (0, 3) satisfying f''(x)=g''(x), f'(1)=4,g'(1)=6,f(2)=3,g(2)=9," then "f(1)-g(1) is -

If f(x) and g(x) are twice differentiable functions on (0,3) satisfying f"(x) = g"(x), f'(1) = 4, g'(1)=6,f(2)=3, g(2) = 9, then f(1)-g(1) is

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < de, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Let a inRR and R and let f:RRrarrRR be given by f(x)=x^5-5x+a Then

    Text Solution

    |

  2. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  3. If f(x) and g(x) are differentiable functions for 0lexle1 such that f(...

    Text Solution

    |

  4. If x=-1 and x=2 are extreme points of f(x)=alphalog|x|+beta|x|^2+x the...

    Text Solution

    |

  5. For every real number x, f(x)=x/(1!)+3/(2!)x^2+7/(3!)x^3+15/(4!)x^4+...

    Text Solution

    |

  6. Let f(x) be a differentiable function in [2,7]. If f(2) = 3 and f'(x)l...

    Text Solution

    |

  7. Suppose that the equation f(x)=x^2+bx+c has two distinct real roots al...

    Text Solution

    |

  8. Let f(x)=inte^x(x-1)(x-2)dx, then f(x) decreases in the interval

    Text Solution

    |

  9. Let R be the set of all real numbers and f:[1,-1]rarrR be defined by ...

    Text Solution

    |

  10. Suppose that f(x) is a differentiable function such that f'(x) is cont...

    Text Solution

    |

  11. Applying Lagrange's Mean Value Theorem for a suitable function f(x) in...

    Text Solution

    |

  12. The angle of intersection between the curves y=[|sinx|+|cosx|]andx^2+y...

    Text Solution

    |

  13. The number of points in (-oo,oo) for which x^2-xsinx-cosx=0 is

    Text Solution

    |

  14. If f(x)=|x|+|x-1|+|x-2|, then

    Text Solution

    |

  15. Let f(x)=xsinpix,xgt0 .Then for all natural number n, f'(x) vanishes a...

    Text Solution

    |

  16. The intercepts on x-axis made by tangents to the curve, oversetxunders...

    Text Solution

    |

  17. The real number k of for which the equation 2x^3+3x+k=0 has two distin...

    Text Solution

    |

  18. If y=sec(tan^(-1)x), then value of dy/dx at x=1 is

    Text Solution

    |

  19. If f(x)=e^x(x-2)^2 then

    Text Solution

    |

  20. Let f(x)=sinx+2cos^2x,pi/4lexle(3pi)/4. then f attains its

    Text Solution

    |