1. Tardigrade
  2. Question
  3. Mathematics
  4. Statement-1: The function f ( x )= ln x is increasing in (0,10) and g ( x )=(1/ x ) is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval (a, b) then its derivative function decreases in the interval (a, b).

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Q. Statement-1: The function $f ( x )=\ln x$ is increasing in $(0,10)$ and $g ( x )=\frac{1}{ x }$ is decreasing in $(0,10)$
Statement-2: If a differentiable function increases in the interval $(a, b)$ then its derivative function decreases in the interval $(a, b)$.

Application of Derivatives

Solution:

Consider the example of $f ( x )= e ^{ x }$ and $f ^{\prime}( x )= e ^{ x }$ both increasing