1. Tardigrade
  2. Question
  3. Mathematics
  4. Statement-1: The function F ( x )= x ln x is increasing in (1 / e , ∞) Statement-2: If f ( x ) and g ( x ) both are increasing in ( a , b ) then f ( x ) ⋅ g ( x ) must be increasing in ( a , b ).

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Q. Statement-1: The function $F ( x )= x \ln x$ is increasing in $(1 / e , \infty)$
Statement-2: If $f ( x )$ and $g ( x )$ both are increasing in $( a , b )$ then $f ( x ) \cdot g ( x )$ must be increasing in $( a , b )$.

Application of Derivatives

Solution:

$f(x)=x$ and $g(x)=x^3$ both are increasing in $(-1,0)$ but $h(x)=x \cdot x^3$ is decreasing.