Find the minimum value of X2 - 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 is A

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

∴ ymin = 2\(\frac{3}{2}\) - 3\(\frac{3}{2}\) + 2

= \(\frac{9}{4}\) - \(\frac{9}{2}\) + 2

= -\(\frac{1}{4}\)