Option 1 : 3/20

Given:

The Polynomial = 1/(3x2 + 4x + 8)

**Concept used:**

If we get minimum value of expression (3x2 + 4x + 8), then we can find maximum value of the expression 1/(3x2 + 4x + 8)

Formula used:

If polynomial ax2 + bx + c, When, a > 0

then Minimum value of polynomial = (4ac – b^{2})/4a

**Calculation:**

If we compared (3x2 + 4x + 8) with ax2 + bx + c, then

a = 3, b = 4 and c = 8

Minimum value of the expression 3x2 + 4x + 8

⇒ {(4 × 3 × 8) - (4)^{2}}/(4 × 3)

⇒ (96 - 16)/12

⇒ 80/12

⇒ 20/3

Maximum value of the expression 1/(2x2 + 5x + 11) = 1/(20/3) = 3/20

**∴ The maximum value of the expression 1/(3x2 + 4x + 8) is 3/20.**