The function h(x) is continuous on the interval [0,6]. If h(0)=–9 and h(6)=11, can you conclude that h(x) is ever equal to 1?
Question
Solution 1
Yes, we can conclude that h(x) is ever equal to 1. This is due to the Intermediate Value Theorem (IVT). The IVT states that if a function is continuous on a closed interval [a,b], then it takes on every value between f(a) and f(b) at some point within the interval.
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