Home
Class 12
MATHS
Show that the function f(x) = 2x+1 is st...

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

Text Solution

AI Generated Solution

To show that the function \( f(x) = 2x + 1 \) is strictly increasing on \( \mathbb{R} \), we need to follow these steps: ### Step 1: Find the derivative of the function The first step is to compute the derivative of the function \( f(x) \). \[ f(x) = 2x + 1 \] ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6a|20 Videos
  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6b|17 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

Show that the function f(x)= x^(2) is strictly increasing function in the interval ]0,infty[ .

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

Show that the function f(x) =- 5x + 2 is strictly decreasing function on R.

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

NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Miscellaneous Exercise
  1. Show that the function f(x) = 2x+1 is strictly increasing on R.

    Text Solution

    |

  2. Using differentials, find the approximate value of each of the follow...

    Text Solution

    |

  3. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

    Text Solution

    |

  4. The two equal sides of an isosceles triangle with fixed base b are ...

    Text Solution

    |

  5. Find the equation of the normal to the curve x^2=4\ y which passes ...

    Text Solution

    |

  6. Show that the normal at any point theta to the curve x=acostheta+at...

    Text Solution

    |

  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

    Text Solution

    |

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

    Text Solution

    |

  9. Find the area of the greatest isosceles triangle that can be inscri...

    Text Solution

    |

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

    Text Solution

    |

  11. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  15. Find the absolute maximum and minimum values of the function f give...

    Text Solution

    |

  16. Show that the altitude of the right circular cone of maximum volume ...

    Text Solution

    |

  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

    Text Solution

    |

  18. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  19. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  20. A cylindrical tank of radius 10 m is being filled with wheat at the r...

    Text Solution

    |

  21. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

    Text Solution

    |