Mathematics

Problem

Which of the following functions on the interval

(0,1)

provides a counterexample to the claim, “If a function is continuous on

(0,1)

and both one–sided limits

\displaystyle\lim_{x\to 0^{+}}f(x)

and

\displaystyle\lim_{x\to 1^{-}}f(x)

exist, then the function must attain a global maximum on

(0,1)

”? a)

f(x)=\sin(\pi x)

\displaystyle f(x)=\frac{1}{x}

f(x)=x

f(x)=x(1-x)