If $\mathrm { P } ( 1 ) = 0$ and $( \mathrm { dP } ( \mathrm { x } ) ) / \mathrm { dx } > \mathrm { P } ( \mathrm { x } )$ for all $\mathrm { x } > 1$ then prove that $\mathrm { P } ( \mathrm { x } ) > 0$ for all $\mathrm { x } > 1$.
The function $f [ 0 , \infty ) \rightarrow [ 0 , \infty )$, defined by $f ( x ) = \frac { x } { 1 + x }$, is
If $\mathrm { P } ( 1 ) = 0$ and $( \mathrm { dP } ( \mathrm { x } ) ) / \mathrm { dx } > \mathrm { P } ( \mathrm { x } )$ for all $\mathrm { x } > 1$ then prove that $\mathrm { P } ( \mathrm { x } ) > 0$ for all $\mathrm { x } > 1$.