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# Solution for 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 - CBSE (Science) Class 12 - Mathematics

#### Question

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

(a) 3
(b) $\frac{3}{4}$

(c) 1
(d) none of these

#### Solution

$(c) 1$

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

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

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

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

$\Rightarrow 2x + 1 = 0$

$\Rightarrow 2x = - 1$

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

$\text { At extreme points } :$

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

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

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

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Solution for question: 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. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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