Home
Class 12
MATHS
Without using the derivative, show that ...

Without using the derivative, show that the function `f(x)=|x|` is (a) strictly increasing in `(0,\ oo)` (b) strictly decreasing in `(-oo,\ 0)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos
  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 Videos

Similar Questions

Explore conceptually related problems

Without using the derivative, show that the function f(x)=|x| is strictly increasing in (0,oo) strictly decreasing in (-oo,0)dot

Without using the derivative show that the function f(x)=7x-3 is strictly increasing function on Rdot

Without using the derivative show that the function f(x)=7x-3 is strictly increasing function on R .

Show that the function f(x) = 2x+1 is strictly increasing on R.

Show that the function f(x)=x^2 is strictly increasing function on (0,\ oo) .

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

Show that the function f(x)=2x+3 is strictly increasing function on Rdot

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increa...

    Text Solution

    |

  2. Show that f(x)=1/(1+x^2) is neither increasing nor decreasing on R ...

    Text Solution

    |

  3. Without using the derivative, show that the function f(x)=|x| is (a) s...

    Text Solution

    |

  4. Without using the derivative show that the function f(x)=7x-3 is stric...

    Text Solution

    |

  5. Find the intervals in which f(x)=-x^2-2x+15 is increasing or decreasin...

    Text Solution

    |

  6. Find the intervals in which the function f(x)=2x^3-9x^2+12 x+15 is inc...

    Text Solution

    |

  7. Find the intervals in which the function f(x)=2x^3+9x^2+12 x+20 is inc...

    Text Solution

    |

  8. Find the intervals in which f(x)=(x+1)^3(x-1)^3 is increasing or decre...

    Text Solution

    |

  9. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

    Text Solution

    |

  10. Find the intervals in which the function f(x)=x^4-(x^3)/3 is increasin...

    Text Solution

    |

  11. Find the intervals in which the function f(x)=log(1+x)-(2x)/(2+x) is i...

    Text Solution

    |

  12. Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasin...

    Text Solution

    |

  13. Determine the intervals in which the function f(x)=x^4-8x^3+22 x^2-24 ...

    Text Solution

    |

  14. Find the intervals for which f(x)=x^4-2x^2 is increasing or decreasing...

    Text Solution

    |

  15. Determine the values of x for which f(x)=(x-2)/(x+2),\ \ x!=-1 is incr...

    Text Solution

    |

  16. Find the intervals in which f(x)=x/2+2/x ,\ \ x!=0 is increasing or de...

    Text Solution

    |

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

    Text Solution

    |

  18. For which values of x , the function f(x)=x/(x^2+1) is increasing and ...

    Text Solution

    |

  19. Find the intervals in which f (x) = 2 log (x - 2) - x^2 + 4x +1 is inc...

    Text Solution

    |

  20. Separate [0,\ pi//2] into subintervals in which f(x)=sin3x is increasi...

    Text Solution

    |