Explain why the function has a zero in the given interval [1,2] f(x)= (1/16) x^4−x^3+3 if f(1) is greater than 0 and f(2) is less than 0 I know it has to do with the intermediate values theorem. Is there anyone that can explain this theorem in plain terms?

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Explain why the function has a zero in the given interval [1,2] f(x)= (1/16) x^4−x^3+3 if f(1) is greater than 0 and f(2) is less than 0 I know it has to do with the intermediate values theorem. Is there anyone that can explain this theorem in plain terms?

Mathematics
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Essentially, the IMV theorem says that for a continuous function on an interval [a, b] if f(a)=y, f(b)=y', and y does not equal y', then there must be some c so that a is less than c, b is greater than c, and f(c) is in between y and y'. So in your problem, use a=1, and b=2. Then, since f(1) is greater than 0, and f(2) is less than 0, 0 is in between f(1) and f(2). So by the IMV, there must be a c so that 1 is less than c is less than 2 such that f(c)=0. Therefore, f(x) has a root in the interval [1, 2]. Is it clearer now?
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