Suppose f is continuous on [1,5] and the only solutions of the equation f (X) = 6 are x=1 and x=4. If f (2) = 8, explain why f (3) >6 ...?

Because since f (2) = 8 and f (4) = 6 and there is no other value between 2 and 4 that gives 6, f must be greater than 6 at 3. if f was lower than 6, it must have skipped over 6, which is not possible since f is continuous