Suppose an extreme point f( 1) = -2 is found, and f(x) is monotonic at (0, 1).

Then, if the limit when x approaches 0 is negative, such as-1, then there is no zero on (0, 1).

But if the limit of x is positive when it approaches 0, such as 2, then there is a zero point on (0, 1).

The tendency +∞ is the same.

Suppose you make sure that f( 1) = -2 and increases monotonically on (0, 1).

You can't just say that there must be a zero on (1, +∞).

Because the function can approach zero infinitely.

So find the limit that X tends to +∞, and see if f(x) is greater than zero when X tends to infinity to determine whether there is zero.