Which of the following functions on the interval provides a counterexample to the…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

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)

(b)

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

(c)

f(x)=x

(d)

f(x)=x(1-x)