Home
Class 12
MATHS
If phi(x) is a differentiable function A...

If `phi(x)` is a differentiable function `AAx in Rand a inR^(+)` such that `phi(0)=phi(2a),phi(a)=phi(3a)and phi(0)nephi(a),` then show that there is at least one root of equation `phi'(x+a)=phi'(x)"in"(0,2a).`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-3 Part II|22 Videos
  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

If phi (x)=phi '(x) and phi(1)=2 , then phi(3) equals

If phi(x) is a differentiable function, then the solution of the different equation dy+{y phi' (x) - phi (x) phi'(x)} dx=0, is

If phi(x) is a differentiable function, then the solution of the different equation dy+{y phi' (x) - phi (x) phi'(x)} dx=0, is

Prove that sin^(2)phi(1+cot^(2)phi)=1

If phi(x) is a differential real-valued function satisfying phi'(x)+2phi(x)le1, then the value of 2phi(x) is always less than or equal to …….

Let phi:[0,1]->[0,1] be a continuous and one-one function. Let phi(0)=0,phi(1)=1,phi(1/2)=p and phi(1/4)=q then

If phi(x) is a diferential real-valuted function satisfying phi'(x)+2phi(x)le1. prove that phi(x)-(1)/(2) is a non-incerasing function of x.

If phi(x)=1/(1+e^(-x)) S=phi(5) +phi(4) +phi(3) + ..+phi(-3) + phi (-4) + phi(-5) then the value of S is

if A ={phi ,{phi}}, then the power set of A is

The solution of differential equation (dy)/(dx)=y/x+(phi(y/x))/(phi'(y/x)) is

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  2. For any acute angled triangleABC,(sinA)/(A)+(sinB)/(B)+(sinC)/(C ) can

    Text Solution

    |

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

    Text Solution

    |

  4. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  5. The cosine of the angle at the vertex of an isosceles triangle having ...

    Text Solution

    |

  6. A cone is made from a circular sheet of radius sqrt3 by cutting out a ...

    Text Solution

    |

  7. Suppose velocity of waves of wave length lambda in the Atlantic ocea...

    Text Solution

    |

  8. Find the minimum distance of origin from the curve ax^(2) +2bxy+ay^(2)...

    Text Solution

    |

  9. Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

    Text Solution

    |

  10. Find which of the two larger log(1+x) " or " (tan^(-1)x)/(1+x).

    Text Solution

    |

  11. Letf'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =...

    Text Solution

    |

  12. if f(x) =(2013) x^(2012) -(2012)x^(2011)-2014x+1007 then show that f...

    Text Solution

    |

  13. A function f is differentiable in the interval 0 le x le 5 such tha...

    Text Solution

    |

  14. Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(...

    Text Solution

    |

  15. f is continuous in [a, b] and differentiable in (a, b) (where a>0 ) su...

    Text Solution

    |

  16. If phi(x) is a differentiable function AAx in Rand a inR^(+) such that...

    Text Solution

    |

  17. Find all the values of the parameter'a' for which the function; f(x)=...

    Text Solution

    |

  18. Let h be a twice continuosly differentiable positive function on an op...

    Text Solution

    |

  19. If the complete set of value(s) of a for which the function f (x) =(a...

    Text Solution

    |

  20. If two curves y=2 sin ((5pix)/6) and y=alphax^(2)-3alphax+2alpha+1 to...

    Text Solution

    |