Prove or disprove the following statement: At any time there are two points on t

Question

Prove or disprove the following statement: At any time there are two points on the 40 degree north latitude circle that have exactly the same temperature and are exactly opposite eachother on the circle (Keep in mind that temperature is a continuous function). If you decided that this is true, are there any other shapes on Earth were this is also true. If you decide the statement is false, are there any shapes on the Earth that for which it would be true? I must explain in words (and possibly graphs) how this works out and I am thinking about using the Intermediate Value Theorem if that is correct. This is for a Calculus 1 class so my professor is not looking for anything too advanced.

Explanation / Answer

first of all you can't apply intermediate value theorem becuase this theorem does not talk about achieving the same value of any function.

this is more about your geography knowledge so YES this is true becuase 40 degree North is the region of Himalaya in Aisa so at the top of himalaya is negative similarly the same temperature is also possible in British region due to warm drift Gulf stream

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