Let be a differentiable function on

MATHEMATICS · Subjective · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

Let

f

be a differentiable function on

0\le x\le 1

. Compare the arc lengths of the following three curves on this interval and list them from shortest to longest (use ties if necessary): I.

C_{1}: y=f(x)

II.

C_{2}: y=-f(x)

III.

C_{3}: y=3f(x)