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2. Relation and Function — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS2. Relation and Function1 Mark
MCQ
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 :
  • ✓
    $\frac{3}{4}$
  • B
    $\frac{3}{2}$
  • C
    $\frac{1}{4}$
  • D
    $\frac{5}{4}$
✓

Answer

Correct option: A.
$\frac{3}{4}$
a
$f ( x )=\left| x ^2- x +1\right|+\left[ x ^2- x +1\right] ; x \in[-1,2]$

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 $x =1 / 2$

$\Rightarrow \text { Minimum } f ( x )=\frac{3}{4}+0$

$=\frac{3}{4}$

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