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CalculusQ&A LibraryA continuous function y = f(x) is known to be negative at x= 4 and positive at x = 9. Why does the equationf(x) = 0 have at least one solution between x= 4 and x= 9? Illustrate with a sketch.Why does the equation f(x) = 0 have at least one solution between x= 4 and x= 9?O A. f(x) = 0 has at least one solution between x= 4 and x= 9 because f is a continuous function on theclosed interval [4, 9], and if y, is any value between f(4) and f(9), then yo = f(c) for some c in [4, 9].O B. f(x) = 0 has at least one solution between x= 4 and x= 9 because f(x) must pass through all valuesbetween f(4) and f(9), regardless of whether f is continuous.OC. f(x) = 0 has at least one solution between x= 4 and x= 9 because all continuous functions have atleast one zero over any nonempty closed interval.Choose a graph below that illustrates the situation.O A.OC.B.D.Ay2-Ay2-2-2-101010Question

Asked Dec 15, 2019

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*show work*

Step 1

Given:

A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

Step 2

Concept used:

Intermediate Value Theorem said that:

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.

Step 3

By Intermediate Value Theorem, f (x) = 0 has at least one solution between...

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