Suppose f is a function defined on [a,b]. Let N be a number with f(a) < N < f(b). Then there...

Question:

Suppose f is a function defined on {eq}[a,b]{/eq}. Let N be a number with f(a) < N < f(b). Then there exists c in (a, b) such that f(c) = N. Why is this statement false?

Intermediate value theorem

Let f(x) is a continuous function defined on {eq}[a,b]{/eq}. Let m be a number with f(a) < m < f(b). Then there exists c in (a, b) such that f(c) = m. Every continuous function attained all the values in between f(a) and f(b).

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Suppose f is a function defined on {eq}[a,b]{/eq}. Let N be a number with f(a) < N < f(b). Then there exists c in (a, b) such that f(c) = N

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Continuity in a Function

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Chapter 2 / Lesson 1
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Continuity is the state of an equation or graph where the solutions form a continuous line, with no gaps on the graph. Learn the concept of continuity, opposed by discontinuity, and examples of both types of functions.


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