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13 Nov 2019
(3 points) Show that the function f(x) = x3 + e5x has exactly one real root First of all, by the Intermediate Value Theorem,f(x) has a solution in the interval (a, b) choose an interval of any length) Now suppose that f (x) has more than one real root. Then by the Mean Value Theorem, between any pair of real roots there must be some point c at which f'(x) is 0 However, we find (you may f'(x) = 3x^2+5e^(5x) and notice that f'(x) is always A. negative OB. positive We conclude that f(x) has exactly one real root
(3 points) Show that the function f(x) = x3 + e5x has exactly one real root First of all, by the Intermediate Value Theorem,f(x) has a solution in the interval (a, b) choose an interval of any length) Now suppose that f (x) has more than one real root. Then by the Mean Value Theorem, between any pair of real roots there must be some point c at which f'(x) is 0 However, we find (you may f'(x) = 3x^2+5e^(5x) and notice that f'(x) is always A. negative OB. positive We conclude that f(x) has exactly one real root
Jean KeelingLv2
8 Nov 2019