Home
Class 12
MATHS
Let f be a function defined on [a, b] su...

Let f be a function defined on `[a, b]` such that `f'(x)>0` for all `x in (a,b)`. Then prove that f is an increasing function on `(a, b)`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.5|47 Videos

  • APPLICATION OF INTEGRALS

    NCERT TELUGU|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Let f:R to R be a function such that |f(x)|le x^(2),"for all" x in R. then at x=0, f is

Let f be function defined for every x , such that f^(11) = -f ,f(0) = 0 , f^(1)(0)=1 then f(x) is equal to

Let f be a function defined on R such that f(x + y) = f (x) + f(y) AA x,y in R . If is continuous at x = 0 , Prove that it is continuous on R .

Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R . Then for all x

Let f (x) be an odd function for continuous at x in R If f(x) is continuous at x = a, prove that it is continous at x=-a

Let f(x) be an even function forall x in R If f(x) is continuous at x = a, prove that it is continuous at x = - a.

Define an onto function. Give one example. (A) A function f:A to B is said to be an onto function if AA b in EE a in A such that f(a)=b (or) if range of f = codomain of f then f is an onto function. Ex. f: R to R such that f(x) = 2x+3

NCERT TELUGU-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. The two equal sides of an isoceles triangle with fixed base b are decr...

    Text Solution

    |

  2. The equation of the normal to the curve x^(2)=4y at (1,2) is

    Text Solution

    |

  3. Show that the normal at any point theta to the curve x = a cos theta +...

    Text Solution

    |

  4. Find the intervals in which the function f given by f(x) = (4sin x-2...

    Text Solution

    |

  5. Find the intervals in which the function f given by f(x) =x^(3) +(1)/(...

    Text Solution

    |

  6. Find the maximum area of an isosceles triangle inscribed in the ellips...

    Text Solution

    |

  7. A tank with rectangular base and rectangular side, open at the top is ...

    Text Solution

    |

  8. The sum of the perimeter of a circle and square is k, where k is some ...

    Text Solution

    |

  9. A window is in the form of a rectangle surmounted by a semi-circular o...

    Text Solution

    |

  10. Find the points at which the function f given by f (x) = (x-2)^(4)(x+1...

    Text Solution

    |

  11. Find the absolute maximum and minimum values of the function f given b...

    Text Solution

    |

  12. Let f be a function defined on [a, b] such that f'(x)>0 for all x in ...

    Text Solution

    |

  13. Show that the height of the cylinder of maximum volume that can be ins...

    Text Solution

    |

  14. Show that height of the cylinder of greatest volume which can be inscr...

    Text Solution

    |

  15. A cylindrical tank of radius 10 m is being filled with wheat at the ra...

    Text Solution

    |

  16. The slope of the tangent to the curve x = t^2+3t-8, y = 2t^2-2t-5at th...

    Text Solution

    |

  17. The line y = mx + 1 is a tangent to the curve y^(2)= 4x if the value o...

    Text Solution

    |

  18. The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

    Text Solution

    |

  19. The equation of the normal to the curve x^(2)=4y at (1,2) is

    Text Solution

    |

  20. The points on the curve 9y^2 = x^3 , where the normal to the curve mak...

    Text Solution

    |