Let a function f:[0,5] → R be continuous, f(1)=3 and F be defined as: F (x)=∫_1^x t^2 g ( t ) dt, where g ( t )=∫_1^t f( u ) du. Then for the…

Let a function $\displaystyle f:[0,5] \rightarrow \mathbf{R}$ be continuous, $\displaystyle f(1)=3$ and F be defined as : $\displaystyle \mathrm{F}(x)=\int_1^x \mathrm{t}^2 \mathrm{~g}(\mathrm{t}) \mathrm{dt}$, where $\displaystyle \mathrm{g}(\mathrm{t})=\int_1^{\mathrm{t}} f(\mathrm{u}) \mathrm{du}$. Then for the function F , the point $\displaystyle x=1$ is :