Find the minimum value of X

^{2}– 3x + 2 for all real values of x-
**A.**

-(frac{1}{4}) -
**B.**

-(frac{1}{2}) -
**C.**

(frac{1}{4}) -
**D.**

(frac{1}{2})

##### Correct Answer: Option A

##### Explanation

y = X^{2} – 3x + 2, (frac{dy}{dx}) = 2x – 3

at turning pt, (frac{dy}{dx}) = 0

∴ 2x – 3 = 0

∴ x = (frac{3}{2})

(frac{d^2y}{dx^2}) = (frac{d}{dx})((frac{d}{dx}))

= 270

∴ y_{min} = 2(frac{3}{2}) – 3(frac{3}{2}) + 2

= (frac{9}{4}) – (frac{9}{2}) + 2

= -(frac{1}{4})