Home
Class 12
MATHS
Show that the function given by f(x)=e^(...

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

Text Solution

Verified by Experts

The correct Answer is:
`2e^(2x)gt 0`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise EXERCISE - 6.3|31 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise EXERCISE - 6.4|23 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER - 6 (SECTION - D)|2 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

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

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

Show that the function given by f(x) = sin x is (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2), pi) (c ) neither increasing nor decreasing in (0, pi) .

Prove that the function f given by f(x) = log sin x is increasing on (0, (pi)/(2)) and decreasing on ((pi)/(2),pi) .

Prove that the function given by f(x)=x^(3)-3x^(2)+3x-100 is increasing in R.

Find the least value of a such that the function given by f(x)=x^(2)+ax+1 is strictly increasing on (1, 2).

f(x)=(x+2)e^(-x) is increasing in ………….

Show that the function f given by f(x)=x^(3)-3x^(2)+4x, x in R is increasing on R.

Show that the function given by f(x)=(log x)/(x) has maximum at x = e.

Find the intervals in which the function f given by f(x)=x^(2)-4x+6 is (a) Increasing (b) Decreasing

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -EXERCISE - 6.2
  1. Show that the function given by f(x)=3x+17 is increasing on R.

    Text Solution

    |

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

    Text Solution

    |

  3. Show that the function given by f(x) = sin x is (a) increasing in ...

    Text Solution

    |

  4. Find the intervals in which the function f given by f(x)=2x^(2)-3x is ...

    Text Solution

    |

  5. Find the intervals in which function f given by f(x)=2x^(3)-3x^(2)-36x...

    Text Solution

    |

  6. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  7. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  8. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  9. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  10. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  11. Show that y=log(1+x)-(2x)/(2+x), x gt -1, is an increasing function of...

    Text Solution

    |

  12. Find the values of x for which y=[x(x-2)]^(2) is an increasing functio...

    Text Solution

    |

  13. Prove that y=(4sin theta)/((2+cos theta))-theta is an increasing funct...

    Text Solution

    |

  14. Prove that the logarithmic function is increasing on (0, oo)

    Text Solution

    |

  15. Prove that the function f given by f(x) = x ^(2) – x + 1 is neither st...

    Text Solution

    |

  16. Which of the following functions is decreasing on (0, (pi)/(2)).

    Text Solution

    |

  17. On which of the following intervals is the function f given by f(x) = ...

    Text Solution

    |

  18. Find the least value of a such that the function given by f(x)=x^(2)+a...

    Text Solution

    |

  19. Let I be any interval disjoint from [-1,1]. Prove that the function f ...

    Text Solution

    |

  20. Prove that the function f given by f(x) = log sin x is increasing on (...

    Text Solution

    |