# Easy to understand, hard to solve

by moham_87
Tags: solve
 Sci Advisor HW Helper P: 2,537 Nice approach, but just because the function is continuous, doesn't mean that it's differentiable. Lets say we have f(x) > 0 and f(y) < 0 with x,y on the interval. let a = min (x,y) and b=max(x,y) Clearly (a,b) is contained in the interval. Therefore f is continuous on [a,b]. It's also clear that 0 is between f(a) and f(a) Then by applying the intermediate value theorem we get hat there must be some point x on the interval [a,b] such that f(x)=0, but this contradicts the hypothesis that $$f(x) \neq 0$$ on the interval.