Answer: f(x) > 0 or f(x) < 0
Reason
"All x in (a,b)" talks about the open interval a < x < b.
If the function is continuous on a < x < b, and f(x)≠0 on this interval, then we know the curve doesn't cross the x axis in this region. Therefore, this piece of the curve is either entirely above the x axis or entirely below the x axis.
Refer to the intermediate value theorem.
- If above the x axis then we go for f(x) > 0 when a < x < b.
- If below the x axis then we go for f(x) < 0 when a < x < b