#### Question

If x lies in the interval [0,1], then the least value of x^{2} + x + 1 is _______________ .

3

`3/4`

1

none of these

#### Solution

1

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

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

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

\[f'\left( x \right) = 0\]

\[ \Rightarrow 2x + 1 = 0\]

\[ \Rightarrow 2x = - 1\]

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

\[\text { At extreme points } : \]

\[ f\left( 0 \right) = 0\]

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

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

Is there an error in this question or solution?

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.