Use the Intermediate Value Theorem to show that cosx=x have at least a solution in [0,π]?

1 Answer
Noah G
Apr 13, 2018

We have:

#cosx - x= 0#

Now let #y = cosx - x#. We see that #y(0) = cos(0) - 0 = 1# and #y(pi) = -1 - pi#

Since #y(pi) < 0 < y(0)#, and #y# is continuous, there must be a value of #x# in #[0, pi]# where #cosx -x = 0#.

Hopefully this helps!

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