GATE EE 2015 Set 1 — Question 22
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Engineering Mathematics → Calculus
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Question
If a continuous function does not have a root in the interval , then which one of the following statements is TRUE?
Correct answer
(C) f(a) · f(b) 0
Solution
According to the Intermediate Value Theorem (IVT), if a continuous function has values of opposite signs at the endpoints of an interval (i.e., ), then there must be at least one root in . If the function has no root in the interval , then must maintain the same sign throughout the interval. Therefore, and must have the same sign, which implies .
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