# 11) Prove that the function f given by $f ( x) = x ^2 - x + 1$  is neither strictly increasing nor decreasing on (– 1, 1).

Given function is,
$f ( x) = x ^2 - x + 1$
$f^{'}(x) = 2x - 1$
Now, for interval $(-1,\frac{1}{2})$ ,  $f^{'}(x) < 0$        and for interval  $(\frac{1}{2},1),f^{'}(x) > 0$
Hence, by this, we can say that  $f ( x) = x ^2 - x + 1$  is neither strictly increasing nor decreasing in the interval (-1,1)

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