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Question
Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).
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Solution
f(x) = x2 - x + 1
f'(x) = 2x - 1
if, f'(x) = 0
2x - 1 = 0
x = `1/2`
x = `1/2` is divided into the intervals (-1, 1), `(-1, 1/2), (1/2, 1)`.
Hence, the function is neither increasing nor decreasing in (-1, 1).
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