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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`<`b1 and f(c)=0

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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