Let $f$ be a function which is continuous and differentiable for all $x$. If $\mathrm{f}(1)=1$ and $\mathrm{f}^{\prime}(x) \leq 5$ for all $x$ in $[1,5]$, then the maximum value of $\mathrm{f}(5)$ is

The function $\mathrm{f}(x)=\sin ^4 x+\cos ^4 x$ increases if

The normal to the curve $x=9(1+\cos \theta)$, $y=9 \sin \theta$ at $\theta$ always passes through the fixed point

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is