Maths-
General
Easy

Question

The function f space left parenthesis x right parenthesis equals 1 plus 1 over x is

  1. always decreasing    
  2. always increasing    
  3. partially decreasing    
  4. partially increasing    

Hint:

We are given a function. We have to find if it's decreasing or increasing. A function is said to be decreasing if it's first order derivative is negative. A function is increasing if it's first order derivative is positive. So, we will take the first order derivative of the given function.

The correct answer is: always decreasing


    The given function is
    f(x) = 1 + 1 over x
    We will find the first order derivative of the given function.
    T h e space g i v e n space f u n c t i o n space c a n space b e space w r i t t e n space a s
f open parentheses x close parentheses equals 1 plus open parentheses x to the power of negative 1 end exponent close parentheses
T a k i n g space t h e space d e r i v a t i v e
f apostrophe left parenthesis x right parenthesis space equals space 0 space minus x to the power of negative 2 end exponent
f apostrophe left parenthesis x right parenthesis space equals space minus 1 over x squared
    The quantity x will be always positive.
    So, the value of the function due to the negative sign will be always negative
    It means f'(x) < 0
    So, the given function is always decreasing.

    We have to see the rules for a increasing and decreasing function.

    Book A Free Demo

    +91

    Grade*

    Related Questions to study