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

Answers (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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