Find the minimum value of X2 – 3x + 2 for all real values of…

Find the minimum value of X² – 3x + 2 for all real values of x

Correct Answer: Option A

Explanation

y = X² – 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})