How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^5 - 3x^4 - 2x^3 + 6x^2 + x + 2# has a zero in the interval [1.7, 1.8]?

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Answer 1 · 2015-10-08T17:34:24

#f# is a polynomial, so it is continuous on the interval #[1.7, 1.8]#

Now convince your reader that #f# at one endpoint is positive and at the other, it it negative.
(Yes, I agree that the arithmetic will be tedious.)