Construct a continuous function on the closed interval that attains its absolute…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Construct a continuous function on the closed interval

[0,2]

that attains its absolute maximum at

x=1

even though the derivative at

x=1

does not exist. Provide an explicit formula for such a function.