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Mathematics, 21.12.2019 03:31, sweetyus06
Use the intermediate value theorem to show that there is a root of the given equation in the specified interval. ex = 8 − 7x, (0, 1) the equation ex= 8 − 7x is equivalent to the equation f(x) = ex− 8 + 7x = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = . since f(0) < 0 < f(1) ,there is a number c in (0, 1) such that f(c) = 0 by the intermediate value theorem. thus, there is a root of the equation ex= 8 − 7x, in the interval (0, 1).
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