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QUESTION
{3 points} Show that the function flfx} = 2x + oos(x} + 5 has exactly one real IDOL First of all, by the Intermeolate 1|ll'alue Theorem, for) has a
Show that the function
f(x)=2x+cos(x)+5
f
(
x
)
=
2
x
+
cos
(
x
)
+
{3 points} Show that the functionflfx} = 2x + oos(x} + 5 has exactly one real IDOL First of all, by the Intermeolate 1|ll'alue Theorem, for) has a solution In the Interyal (o, b} = {you may choose an interval of any length} Now suppose that f (1:) has more than one real root. Then by the Mean Value Theorem, between any pair of real roots therernust be some point t? at 1which f ’ (12} Is Howeyer. we findf’ix} =and notice that f '(x) is always A. posItiye..“-. B. negative. We conclude that fix} has exactly one real root.