Continuity and DifferentiabilityHard
Question
Let f be a differentiable function on the open interval (a, b). Which of the following state meets must be true ?
(i) f is continuous on the closed interval [a, b]
(ii) f is bounded on the open interval (a, b)
(iii) If a < a1 < b1 < b and f(a1) < 0 < f(b1), then there is a number c such that a1 < c < b1 and f(c) = 0
(i) f is continuous on the closed interval [a, b]
(ii) f is bounded on the open interval (a, b)
(iii) If a < a1 < b1 < b and f(a1) < 0 < f(b1), then there is a number c such that a1 < c < b1 and f(c) = 0
Options
A.(i) and (ii) only
B.(i) and (iii) only
C.(ii) and (iii) only
D.only (iii)
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