Home
Class 12
MATHS
if f (x) satisfies condition in Rolle's...

if f (x) satisfies condition in Rolle's theorem then show that between two consecutive zeros of f(x) there lies at most one zero of f(x).

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise -1A|5 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise -1B|6 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise High Level Problems (HLP)|33 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

If f(x) satisfies the condition for Rolle's heorem on [3,5] then int_(3)^(5) f(x) dx equals

If y=f(x) satisfies has conditions of Rolle's theorem in [2, 6], then int_(2)^(6)f'(x)dx is equal to

If f(x) satisfying the conditions of Rolle's theorem in [1,2] and f(x) is continuous in [1,2] then int_(1)^(2) f'(x) dx =

If f(x)=x^(3)+bx^(2)+ax satisfies the conditions on Rolle's theorem on [1,3] with c=2+(1)/(sqrt(3))

If f(x) satifies of conditiohns of Rolle's theorem in [1,2] and f(x) is continuous in [1,2] then :.int_(1)^(2)f'(x)dx is equal to

If f(x)=2(x-1)^(2), x in [0,2] then Rolle's theorem satisfies at

For the function f(x)=e^(cos x), Rolle's theorem is

If f(x)=x^(2)-5x+9, x in [1,4], then Rolle's theorem satisfies at

If f(x) = 4^(sin x) satisfies the Rolle's theorem on [0, pi] , then the value of c in (0, pi) for which f'(c ) = 0 is

The function f(x)=x^(3)-6x^(2)+ax+b satisfy the conditions of Rolle's theorem in [1,3] .The values of a and b are

RESONANCE-APPLICATION OF DERIVATIVES-Self Practice Problems
  1. For each of the following graph comment on monotonically of f(x) ...

    Text Solution

    |

  2. Let f(x)=x^3-3x^2+ 3x + 4, comment on the monotonic behaviour of f(x) ...

    Text Solution

    |

  3. Draw the graph of function f(x)={underset([x] " "1 le x le 2)(x " ...

    Text Solution

    |

  4. In each of following graphs identify if x= a is point of local maxi...

    Text Solution

    |

  5. Examine the graph of following functions in each case identify the p...

    Text Solution

    |

  6. Find the points of local maxima or minima of following functions...

    Text Solution

    |

  7. Let f(x) =x^(3) =x^(2) -x-4 (i) find the possible points of maxim...

    Text Solution

    |

  8. Let f(x) =x +(1)/(x). find local maximum and local minimum value ...

    Text Solution

    |

  9. if f(x) ={underset( cos x " "x le 0)((x+lambda)^(2) " " x lt 0). ...

    Text Solution

    |

  10. Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of criti...

    Text Solution

    |

  11. Find the two positive numbers x and y whose sum is 35 and the ...

    Text Solution

    |

  12. A square piece of tin of side 18 cm is to be made into a box withou...

    Text Solution

    |

  13. A square piece of tin of side 18 cm is to be made into a box withou...

    Text Solution

    |

  14. The maximum distance of the centre of the ellipse x^2/(81)+y^2/(25)=1 ...

    Text Solution

    |

  15. A line is drawn passing through point P(1,2) to cut positive coord...

    Text Solution

    |

  16. Two towns A and B are situated on the same side of a straight road at ...

    Text Solution

    |

  17. if f (x) satisfies condition in Rolle's theorem then show that betw...

    Text Solution

    |

  18. Show that for any real numbers lambda, the polynomial P(x)=x^7+x^3+lam...

    Text Solution

    |

  19. Using LMVT, prove that if two functions have equal derivatives at all ...

    Text Solution

    |

  20. if a function f is (i) continuous on [a,b] (ii) derivable on (a,b...

    Text Solution

    |