1.

What is the maximum value of expression x2/(2x + 3)?

Answer» Correct Answer - Option 3 : Cannot be determined

GIVEN:

Expression = x2/(2x + 3)

CONCEPT:

Maximum value of the expression

CALCULATION:

Let k = x2/(2x + 3)

⇒ k (2x + 3) = x2

⇒ 2kx + 3k = x2

⇒ x2 – 2kx – 3k = 0

For all real value of ‘x’, D ≥ 0

D = b2 – 4ac ≥ = 0

After comparing above equation with ax2 + bx + c = 0

a = 1, b = -2k and c = -3k

⇒ (-2k)2 – 4 × 1 × (-3k) ≥ 0

⇒ 4k2 + 12k ≥ 0

⇒ 4k (k + 3) ≥ 0

⇒ k ≥ 0 and k ≤ -3

⇒ k = (-∞, -3] ∪ [0, ∞)

Hence, maximum value of the expression cannot be determined.


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