Find the minimum value of X2 - 3x 2 for all rea... - JAMB Mathematics 1997 Question
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
\(\frac{1}{2}\)
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Correct Option: 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})
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