Assertion (A): The function f ( x )= x^2- x +1 is strictly increasing on (-1,1). Reason (R): If f ( x ) is continuous on [ a, b ] and derivable on (…

Assertion (A): The function $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x}^2-\mathrm{x}+1$ is strictly increasing on $\displaystyle (-1,1)$. Reason (R): If $\displaystyle \mathrm{f}(\mathrm{x})$ is continuous on $\displaystyle [\mathrm{a}, \mathrm{b}]$ and derivable on $\displaystyle (\mathrm{a}, \mathrm{b})$, then $\displaystyle \mathrm{f}(\mathrm{x})$ is strictly increasing on $\displaystyle [\mathrm{a}, \mathrm{b}]$ if $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})>0$ for all $\displaystyle \mathrm{x} \in(\mathrm{a}, \mathrm{b})$.