Question #3ded9

1 Answer
Apr 1, 2017

Let f(x)=xcosx.

We know that f is continuous on [0,π2] since it is the difference of two continuous functions x and cosx, and

f(0)=1<0<π2=f(π2).

By Intermediate Value Theorem, there exists c(0,π2) s.t.
f(c)=ccos(c)=0, which means that c=cos(c).

Hence, x=cosx has a solution c(0,π2).