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Let f be a differentiable function on th...

Let f be a differentiable function on the open interval(a, b). Which of the following statements 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 < b, and f(c) = 0
(a)Only I and II
(b)Only I and III
(c)Only II and III
(d)Only III

A

Only I and II

B

Only I and III

C

Only II and III

D

Only III

Text Solution

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The correct Answer is:
D
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