JEE Mains · Maths · STD 11- 2. Relation and Function
The absolute minimum value, of the function \(f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right], \quad\) where \([t]\) denotes the greatest integer function, in the interval \([-1,2]\), is :
- A \(\frac{3}{4}\)
- B \(\frac{3}{2}\)
- C \(\frac{1}{4}\)
- D \(\frac{5}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(f ( x )=\left| x ^2- x +1\right|+\left[ x ^2- x +1\right] ; x \in[-1,2]\) Let \(g(x)=x^2-x+1\) \(=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\) \(\because\left| x ^2- x +1\right| \text { and }\left[ x ^2- x +2\right]\) Both have minimum value at \(x =1 / 2\)…
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