Next Problem (2 points) Find the absolute maximum and absolute minimum values of the function f(t)=1-√√t on the interval

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Next Problem (2 points) Find the absolute maximum and absolute minimum values of the function f(t)=1-√√t on the interval [-5, 1]. Enter only the y-value as your answer. Absolute maximum: o Absolute minimum: -0.38487

(4 points) Show that the function f(x) = cos(x) - 2x has exactly one real root. First of all, by the Intermediate Value Theorem, f(x) has a solution in the interval (a, b) = (you may 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 However, we find f'(x) = and notice that f'(x) is always OA. positive. OB. negative. We conclude that f(x) has exactly one real root.

f(x) = x² + ³x has exactly one real root. First of all, by the Intermediate Value Theorem, f(x) has a solution in the interval (a, b) = (you may 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 However, we find f'(x) = and notice that f'(x) is always A. positive. B. negative. We conclude that f(x) has exactly one real root.

(4 points) Show that the function f(x) = 6x + 5 cos(x) + 5 has exactly one real root. First of all, by the Intermediate Value Theorem, f(x) has a solution in the interval (a, b) = (you may 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 However, we find f'(x) = and notice that f'(x) is always A. positive. B. negative. We conclude that f(x) has exactly one real root.