A) Increases on \[\left[ \frac{1}{2},1 \right]\]
B) Decreases on \[\left[ 0,\frac{1}{2} \right]\]
C) Increases on \[\left[ 0,\frac{1}{2} \right]\]
D) Neither increases nor decreases on \[[0,\,\,1]\]
Correct Answer: C
Solution :
Given function \[f(x)={{x}^{2}}-x+1,0\le x\le 1\] For strictly increasing function \[f'(x)>0\] \[2x-1>0\] \[x>\frac{1}{2}\] Hence, function is not increasing in\[\left[ 0,\frac{1}{2} \right]\].
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