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

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

Text Solution

Verified by Experts

The correct Answer is:
`x_(1), x_(2)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|85 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise EXERCISE - 6.5|47 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

Let f be an even function and f'(0) exists, then f'(0) is

Prove that f(x)= 2x-|x| is a continuous function at x= 0.

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f : R rarr R be the function defined by f(x) = 1/(2-cosx),AA x inR . Then , find the range of f .

Without using differentiation, prove that f(x)=ax+b , where a gt 0 is strictly increasing function AA x in R .

Is the function defined by f(x)= |x|, a continuous function

let f: RrarrR be a function defined by f(x)=max{x,x^3} . The set of values where f(x) is differentiable is:

Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R . Write f^(-1) .

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx)

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a, (a)f(x) is a periodic function (b)f(x) is a constant function (c) f(x)=1/2 (d) f(x)=(cosx)/2

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -MISCELANEOUS EXERCISE - 6
  1. Find the intervals in which the function f given f(x)=x^(3)+(1)/(x^(3)...

    Text Solution

    |

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

    Text Solution

    |

  3. A tank with rectangular base and rectangular sides, open at the top is...

    Text Solution

    |

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

    Text Solution

    |

  5. A window is in the form of a rectangle surmounted by a semicircular op...

    Text Solution

    |

  6. A point on the hypotenuse of a triangle is at distance a and b from th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Find the absolute maximum and minimum values of the function given by ...

    Text Solution

    |

  11. Show that the altitude of the right circular cone of maximum volume th...

    Text Solution

    |

  12. Let f be a function defined on [a,b] such that f'(x)gt 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-5 at t...

    Text Solution

    |

  17. The line y= m x +1 is a tangent to the curve y^2 =4 x if th...

    Text Solution

    |

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

    Text Solution

    |

  19. The normal to x^(2)=4y passing through (1, 2) has equation ……….

    Text Solution

    |

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

    Text Solution

    |