Discussion

Question:

Find the maximum value of the expression: $\frac{1}{2 x^{2} + 3 x + 10}$ .

Explanation:

The maximum value of the expression $\frac{1}{2 x^{2} + 3 x + 10}$ will occur when 2x² + 3x + 10 is minimum.

2x² + 3x + 10 is minimum at x = -(3/4) = -3/4

∴ Minimum value of 2x² + 3x + 10 = $2 {(\frac{- 3}{4})}^{2}$ + $3 (\frac{- 3}{4})$ + 10

= $\frac{9}{8}$ - $\frac{9}{4}$ + 10

= $- \frac{9}{8}$ + 10

= $\frac{71}{8}$

∴ The maximum value of $\frac{1}{2 x^{2} + 3 x + 10}$ = $\frac{1}{71 / 8}$ = $\frac{8}{71}$

Hence, option (d).

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