# If x lies in the interval [0, 1], then the least value of x^2 + x + 1 is A. 3 B. 3/4. C. 1 D. none of these

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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

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Option : (C)

f(x) = x2 + x + 1

f’(x) = 2x + 1

f’(x) = 0

⇒ 2x + 1 = 0

⇒ x = -$\frac{1}{2}$

At extreme points,

f(0) = 0

f(1) = 1 + 1 + 1 > 0

So,

x = 1 is a least value.