Statement 1: The function x^2( e^x+ e^-x) is increasing for all x>0. Statement 2: The functions x^2 e^x and x^2 e^-x are increasing for all x>0 and…

Statement $\displaystyle 1$ : The function $\displaystyle x^2\left(\mathrm{e}^x+\mathrm{e}^{-x}\right)$ is increasing for all $\displaystyle x>0$.Statement $\displaystyle 2$ : The functions $\displaystyle x^2 \mathrm{e}^x$ and $\displaystyle x^2 \mathrm{e}^{-x}$ are increasing for all $\displaystyle x>0$ and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b).