Thread: Continuous Functions

Originally Posted by acevipa

I'll show you number 1.

Define the function and note it is continuous. Then, we have and . Depending on the size of f(1/2) relative to f(0)=f(1), we either have g(a) goes from negative to positive or positive to negative. In either case, we have that g(a) = 0 at some point from 0 to 1/2. This shows number 1.