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Question -

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



Answer -

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 isstrictly decreasing in interval

However, in interval

Therefore, f isstrictly increasing in interval

Hence, f is neitherstrictly increasing nor decreasing in interval (−1, 1).

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