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

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

Text Solution

Verified by Experts

`f(x) = 3 x + 17`
`rArr f'(x) = 3 gt 0" "forall x in R`
`:. F(x) ` is strictly increasing on R.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6.3|27 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6.4|9 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6.1|18 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

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

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

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

Prove that the function given by f(x)=2x^(3)-6x^(2)+7x is strictly increasing in R.

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

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

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

Prove that the function defined by f(x)=e^(x) is strictly increasing in R

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

NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Exercise 6.2
  1. Show that the function given by f (x) = 3x + 17is strictly increasing...

    Text Solution

    |

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

    Text Solution

    |

  3. Show that f(x)=sinx is increasing on (0,\ pi//2) and decreasing on (pi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Prove that y = ( 4 sin theta)/(2 + cos theta) - theta is an increasin...

    Text Solution

    |

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

    Text Solution

    |

  11. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

    Text Solution

    |

  12. Which of the following functions are strictly decreasing on [0,pi/2](...

    Text Solution

    |

  13. On which of the following intervals is the function x^(100)+sinx-1 dec...

    Text Solution

    |

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

    Text Solution

    |

  15. Let I be any interval disjoint from (1, 1). Prove that the function f...

    Text Solution

    |

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

    Text Solution

    |

  17. Prove that the function f given by f(x) = log | cos x|" is decreasing ...

    Text Solution

    |

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

    Text Solution

    |

  19. The interval in which y=x^2""e^(-x) is increasing is

    Text Solution

    |