Question

Prove that the function f given by f(x) = x² − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).

Answer 1

The given function is f(x) = x² − x + 1.

The pointdivides the interval (−1, 1) into two disjoint intervals i.e.,

Now, in interval

Therefore, f is strictly decreasing in interval.

However, in interval

Therefore, f is strictly increasing in interval.

Hence, f is neither strictly increasing nor decreasing in interval (−1, 1).