Prove x^3 = cosx + 16
Not sure how to go about this one? Any suggestions?
Having graphed it, I see that there is an intersection at x slightly larger than 2. Using that, I can give a more formal proof by noting that while is greater than 15.5 and that while is only slightly larger than 15.
That is, while . Since and cos(x)+ 16 are continuous functions, there must be x between 2 and 3 such that .