f has a maximum on [0,1].

f does not have a maximum on [0,\frac{1}{\pi}].

f does not have a maximum on [0,\frac{1}{2}].

\sup (f([0,\frac{1}{\pi}]))=\frac{1}{\pi^2}.

\sup(f([0,\frac{1}{2}]))=\frac{1}{4}.

f has a minimum on [0,1].

f is differentiable at 0.

f is differentiable at 1.

f is continuous at 0.

f is continuous at 1.

L'Hopital rule can be applied to find \lim_{x\to 0^+}\frac{f(x)}{g(x)}

L'Hopital rule can be applied to find \lim_{x\to 0^+}\frac{g(x)}{f(x)}

f'(x)\neq 0 on (0,1).

g is differentiable on [0,1].

\lim_{x\to 0^+}\frac{f(x)}{g(x)}=\infty

f is differentiable on [0,1].

\lim_{x\to 0^+}\frac{g(x)}{f(x)}=0

 \lim_{x\to 0^+}\frac{f'(x)}{g'(x)} exists

f,g are continuous on [0,1].

 \lim_{x\to 0^+}\frac{g'(x)}{f'(x)} exists

g'(x)\neq 0 on (0,1).

f,g are differentiable on (0,1).