A function is continuous on a closed interval and has exactly one critical point in

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A function

f

is continuous on a closed interval

[a,b]

and has exactly one critical point

c

(a,b)

. In one or two sentences, explain why verifying that

f

has a relative minimum at

c

is sufficient to conclude that

f(c)

is the absolute minimum on

[a,b]