Show that if 0 ≤ f' (x) ≤ 1 for all x, then the arc length of y = f (x) over [a, b] is at most √2(b − a). Show that for f (x) = x, the arc length equals √2(b − a).
Show that if 0 ≤ f' (x) ≤ 1 for all x, then the arc length of y = f (x) over [a, b] is at most √2(b − a). Show that for f (x) = x, the arc length equals √2(b − a).
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