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

Assessment: JAMB UTME - Mathematics - 1997 Subject: General Mathematics

Question 1 Report

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\frac{1}{4}

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\frac{1}{2}

\frac{1}{4}

\frac{1}{2}

Answer Details

y = X2 - 3x + 2, $\frac{d y}{d x}$ = 2x - 3
at turning pt, $\frac{d y}{d x}$ = 0
∴ 2x - 3 = 0
∴ x = $\frac{3}{2}$
$\frac{d^{2} y}{d x^{2}}$ = $\frac{d}{d x}$ ( $\frac{d}{d x}$ )
= 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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