Question

True or false statement?

If `f'(x)!=0` and `f` is strictly monotone in an interval `[a,b]subeRR` then `f(x)>0` or `f(x)<0`

Answer 1

False

Explanation:

Consider a counterexample:

Let `f(x)=x(x-1)` on `[3/4, 7/4]`. Indeed, we have `f'(x)!=0` and `f` monotone on this interval, but we observe that `f(1)=0`.

So the statement is false.