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EleoNora [17]
3 years ago
10

A continuous function y=f(x) is known to be negative at x=0 and positive at x=1. Why does the equation f(x)=0 have at least one

solution between x=0 and x=1?
Mathematics
2 answers:
olga55 [171]3 years ago
8 0
Because the y values change signs from negative to positive which means the graph had to cross over the x-axis thereby creating a solution.
FromTheMoon [43]3 years ago
8 0

Answer:

Givens

It's known that the function is negative at x=0 and positive at x=1.

To answer this question, we need to use the Intermediate Value Theorem, which states:

  • If f(x) is a continuous function on [a, b], then for every k between f(a) and f(b), there exists a value c belongs to (a, b) such that f(c) = k.

Therefore, the function f(x)=0 hast a least one solution between x=0 and x=1 because the function is continuous in the closed interval [0,1], and based on the intermediate value theorem, if there exist a value inside this interval, then there's at least one solution there.

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