PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# If X Lies in the Interval [0,1], Then the Least Value of X2 + X + 1 is (A) 3 (B) 3 4 (C) 1 (D) None of These - PUC Karnataka Science Class 12 - Mathematics

#### Question

If x lies in the interval [0,1], then the least value of x2 + x + 1 is _______________ .

• 3

• 3/4

• 1

• none of these

#### Solution

1

$\text { Given: } f\left( x \right) = x^2 + x + 1$

$\Rightarrow f'\left( x \right) = 2x + 1$

$\text { For a local maxima or a local minima, we must have }$

$f'\left( x \right) = 0$

$\Rightarrow 2x + 1 = 0$

$\Rightarrow 2x = - 1$

$\Rightarrow x = \frac{- 1}{2} \not\in \left[ 0, 1 \right]$

$\text { At extreme points } :$

$f\left( 0 \right) = 0$

$f\left( 1 \right) = 1 + 1 + 1 = 3 > 0$

$\text { So, x = 1 is a local minima }.$

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Solution If X Lies in the Interval [0,1], Then the Least Value of X2 + X + 1 is (A) 3 (B) 3 4 (C) 1 (D) None of These Concept: Graph of Maxima and Minima.
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