starting from 0 degree latitude and proceeding in a westerly direction along the equator, let T(x) be the temperature at the point x at any given time. Assuming T(x) is a continuous function of x, show that at any fixed time. there are at least 2 diametrically opposite points on the equator, say a and a+180, that have exactly the same temperature.
Hint: construct a function F(x) using t(x) and use the intermediate value theorem.
all i can come up is that we need to prove:
T(x) = T(x+180)
which is T(x) - T(x+180) = 0
let f(x) = T(x) - T(x+180)
if we can prove that f(x) has a root, then T(x) can = T(x+180)
since T(x) and T(x+180) are continous function, so f(x) as well.
that is as far as i can go
how can i determine where f(x) is negative and positive ???