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

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

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