The maximum value of the function

f(x) = 2 + x – x

f(x) = 2 + x – x

^{2}is-
**A.**

9/4 -
**B.**

7/4 -
**C.**

3/2 -
**D.**

1/2

##### Correct Answer: Option A

##### Explanation

f(x) = 2 + x – x^{2}^{dy}/_{dx} = 1-2x

As ^{dy}/_{dx} = 0

1-2x = 0

2x = 1

x = ^{1}/_{2}

At x = ^{1}/_{2}

f(x) = 2 + x – x^{2}

= 2 + ^{1}/_{2} -(^{1}/_{2})^{2}

= 2 + ^{1}/_{2} – ^{1}/_{4}

= (8+2-1) / 4 = ^{9}/_{4}