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

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

Answer 1

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.