Question

Find the greatest value of

$\frac{x + 2}{2 {x}^{2} + 3x + 6 }$

for real values of 'x'.


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Answer 1

So if,

$\frac{x + 2}{2 {x}^{2} + 3x + 6 }$ = 1/3 (maximum)

=) 2yx² + x(3y-1) + (6y-2) = 0

=) 2(1/3)x² + x(3*1/3 - 1) + (6*1/3 - 2) =0

=) 2/3 x² + x(1-1) + (2-2) = 0

=) x² = 0 * 3/2

=) x = 0.

Answer 2

Refer the attachment

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