Home
Class 12
MATHS
Show that f(x)=(1/2)^x is strictly decre...

Show that` f(x)=(1/2)^x` is strictly decreasing on R.

Text Solution

Verified by Experts

We have `f(x)=(1/2)^xthereforef(x)=2^-x`
therefore`f.(x)=(2^-xlog2)(-1)=-log2/2^x`
`x in R implies 2^x>0implies log2/2^x0implies - log2/2^x<0implies f.x<0`.
therefore f(x) is strictly decreasing on R.
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVE

    PATHFINDER|Exercise QUESTION BANK|327 Videos

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos

Similar Questions

Explore conceptually related problems

Show that : tanx -x is strictly increasing on (0,pi/2) .

If f(x)=mu x-sin x is strictly increasing then

Find the interval in which f(x)=x^3-3x^2-9x+30 is strictly increasing or strictly decreasing.

A function f(x) is defined in a lt x lt b and a lt x_(1) lt x_(2) lt b , then f(x) is strictly monotonic decreasing in a le x le b when-

If f(x)= int e^(x)(x-1)(x-2)dx , then show that f(x) is a decreasing function 1 lt x lt 2 .

Prove that f(x)= a^x , 0 < a < 1 , is decreasing in R.

The function f(x) = ax + b is strictly increasing for all real x if

Let f(x)=3x+5 then show f(x) is strictly increasing and f^(-1)(x) exists and is strictly increasing for "x"inR

Show that the function f(x)=(3x+5)/(x+2) is strictly monotonic increasing in [0, oo) .

Prove that the function f(x)=(log)_e(x^2+1)-e^(-x)+1 is strictly increasing AAx in Rdot

PATHFINDER-APPLICATION OF DERIVATIVES-QUESTION BANK
  1. At what point of the ellipes 16x^2+9y^2=400, does the ordinate decrea...

    Text Solution

    |

  2. A particle moves along the curve 6y = x^(3) +2. Find the points on the...

    Text Solution

    |

  3. A ladder 16 cm long is leaning against a wall. The bottom of the ladde...

    Text Solution

    |

  4. Water is leaking from a conical funnel at the rate of 5 cm^3/sec. If t...

    Text Solution

    |

  5. Show that f(x)=(1/2)^x is strictly decreasing on R.

    Text Solution

    |

  6. Show that : tanx -x is strictly increasing on (0,pi/2).

    Text Solution

    |

  7. Show that the following function is strictly increasing :f(x)=x^2,x>0.

    Text Solution

    |

  8. Find the intervals on which the following function is strictly increas...

    Text Solution

    |

  9. Find the intervals on which the following function is strictly increa...

    Text Solution

    |

  10. Find the intervals on which the following function is strictly increa...

    Text Solution

    |

  11. FInd the slopes of the tangents and normals to the following curve: x=...

    Text Solution

    |

  12. Show that the tangents to the curve y=x^2-5x+6 at the point (2,0) and ...

    Text Solution

    |

  13. Find the equations of the tangent and normal to the curve y=x^2-4x-5 a...

    Text Solution

    |

  14. Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (...

    Text Solution

    |

  15. For the curve y = 4x^(3) – 2x^(5) , find all the points at which the t...

    Text Solution

    |

  16. FInd the equation of the normal to the curve 3x^2-y^2=8 which is para...

    Text Solution

    |

  17. Show that the curve xy=a^2 and x^2+y^2=2a^2 touch each other.

    Text Solution

    |

  18. Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^...

    Text Solution

    |

  19. Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2...

    Text Solution

    |

  20. If y=x^4-10 and if x change from 2 to 1.99, what is the approximate c...

    Text Solution

    |