How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = -1 + 3 cos x# has a root in the interval [0, 5pi/2]?

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Answer 1 · 2015-09-26T11:59:27

See explanation below.

#f# is continuous on #[0, (5pi)/2]# #" "# (In fact, is continuous on #RR#.)

#f(0)=2 # and # f((5pi)/2)=-1#

So, #0# is between #f(0) # and # f((5pi)/2)#.

Therefore, by the Intermediate Value Theorem, there is a number #c# in the interval, with #f(c) = 0#