Prove that at any given moment, there exists a pair of diametrically opposed points on the equator of the Earth that have the same temperature.

Question

Question: Prove that at any given moment, there exists a pair of diametrically opposed points on the equator of the Earth that have the same temperature. Use the Intermediate Value Theorem.

Now I've been kinda struggling with how to deal with the Intermediate Value Theorem and I have no idea where to even start on this one.

Answer 1

Consider the function on the equator given by the difference of the temperature at that point and the temperature at its antipodal point. What is the value of that function at a point whose temperature is the same as that of its antipodes?