If f'(x) has no roots, does that mean f(x) will always have at least one root - Maths - Application of Derivatives

Question

If f'(x) has no roots, does that mean f(x) will always have at
least one root?

Rishabh Mittal · Accepted Answer

Dear Student,

No, it is not true
For example,fx=5f'x=0Here f x and f'x both dont have roots

Regards

If f'(x) has no roots, does that mean f(x) will always have at least one root?