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

`f(x)` and `g(x)` are differentiable functions for `0 le x le 2` such that `f(0)=5, g(0)=0, f(2)=8, g(2)=1`. Show that there exists a number c satisfying `0 lt c lt 2` and `f'(c)=3g'(c)`.

Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 3 ( Subjective ) COMPREHENSION|4 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-I ) Previous Year|4 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-II) ( Multiple Correct ) MIXED PROBLEMS|5 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

f(x) and g(x) are differentiable functions for 0 <= x <= 2 such that f(0) = 5, g(0) = 0, f(2)= 8,g(2) = 1. Show that there exists a number c satisfying 0 < c < 2 and f'(c)=3 g'(c).

If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(0)=2,g(0) = 0,f(1)=6,g(1)=2 , then in the interval (0,1)

Let f and g be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6 and g(1)=2. Show that there exists c in(0,1) such that f'(c)=2g'(c)

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

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

Let f(x) and g(x) be differentiable for 0<=x<=2 such that f(0)=2,g(0)=1, and f(2)=8. Let there exist a real number c in [0,2] such that f'(c)=3g'(c). Then find the value of g(2)

Let f(x) and g(x) be differentiable for 0<=x<=1 such that f(0)=0 g(0)=6 .let there exists a real number c in (0 1) such that f'(c)=2g'(c) then the value of g(1) must be

Let f(x) and g(x) be differentiable for 0<=x<=1, such that f(0)=0,g(0)=0,f(1)=6. Let there exists real number c in (0,1) such taht f'(c)=2g'(c)* Then the value of g(1) must be 1( b) 3(c)-2(d)-1

MOTION-MONOTONOCITY-Exercise - 3 ( Subjective )
  1. Find the intervals of monotonocity for the following functions & repre...

    Text Solution

    |

  2. Let f(x)={:{(x^(2),x ge 0),(ax, x lt 0):}. Find real values of a such...

    Text Solution

    |

  3. If f(x) = x^(3) + (a – 1) x^(2) + 2x + 1 is strictly monotonically in...

    Text Solution

    |

  4. Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x...

    Text Solution

    |

  5. Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1)...

    Text Solution

    |

  6. Using monotonicity prove that x lt - ln (1-x) lt x (1-x)^(-1) for ...

    Text Solution

    |

  7. Using monotonicity prove that (x)/(1-x^(2)) lt tan^(-1)x lt x for...

    Text Solution

    |

  8. Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\...

    Text Solution

    |

  9. Verify Rolles theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}...

    Text Solution

    |

  10. Using Rolle's theorem prove that the equation 3x^2 + px - 1 = 0 has th...

    Text Solution

    |

  11. f(x) and g(x) are differentiable functions for 0 le x le 2 such that ...

    Text Solution

    |

  12. Show that the lagranges mean value theorem is not applicable to the...

    Text Solution

    |

  13. If a, b are two real numbers with a lt b show that a real number 'c' ...

    Text Solution

    |

  14. Using LMVT prove that : (a) tan x gt x in (0, pi/2), (b) sin x l...

    Text Solution

    |

  15. Construct the graph of the function f(x)=-|(x^(2)-9)/(x+3)-x+(2)/(x-...

    Text Solution

    |

  16. Show that exactly two real values of x satisfy the equation x^2= xsinx...

    Text Solution

    |

  17. If g(x) is monotonically increasing and f(x) is monotonically decreasi...

    Text Solution

    |

  18. For x in (0, pi/2) identify which is greater (2 sin x + tan x ) or ...

    Text Solution

    |

  19. Using monotonocity find range of the function f(x)=sqrt(x-1)+sqrt(6...

    Text Solution

    |

  20. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

    Text Solution

    |