Home
Class 12
MATHS
Show that the function f(x)=a^x ,\ a >1 ...

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

Text Solution

Verified by Experts

Given,`f(x)=a^x`
`f′(x)=a^xloga`
function is increasing on R.
`a^xloga>0`
...
Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos
  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x) = e^(x) is strictly increasing on R.

Show that the function given by f(x)=e^(2x) is strictly increasing on R

Prove that the function f(x) = 10^(x) is strictly increasing on R

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

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

If a is real number such that 0 lt alt 1 , show that the function f(x) = a^(x) is strictly decreasing on R.

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

Show that the function f(x) = 5x - 2 is a strictly increasing function on R

Show that the function given by f(x)=7x-3 is strictly increasing on R .

Show that the function given by f(x)=3x+17 is strictly increasing on R .

RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that the function f(x)=2x+3 is strictly increasing function on...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Show that the function f(x)=-3x+12 is strictly decreasing function ...

    Text Solution

    |

  5. Show that the function f(x)=a^x ,\ 0<a<1 is strictly decreasing on R .

    Text Solution

    |

  6. Show that the function f(x)=x^2 is a strictly decreasing function o...

    Text Solution

    |

  7. Show that the function f(x)=x^2 is neither strictly increasing nor ...

    Text Solution

    |

  8. Prove that the function f(x)=(log)e x is increasing on (0,\ oo) .

    Text Solution

    |

  9. Prove that the function f(x)=(log)a x is increasing on (0,\ oo) if a >...

    Text Solution

    |

  10. Prove that f(x)=a x+b , where a ,\ b are constants and a >0 is an incr...

    Text Solution

    |

  11. Prove that f(x)=a x+b , where a ,\ b are constants and a<0 is a decrea...

    Text Solution

    |

  12. Show that f(x)=1/x is a decreasing function on (0,\ oo) .

    Text Solution

    |

  13. Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increa...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |