Explanation:

y = 6−x

So xy = x(6−x) = 6x−x∗x

First derivative (with respect to x) = 6–2x

Second derivative = -2

So making first derivative equal to zero,

6–2x = 0

2x = 6

x = 3

So y = 6−x=6–3=3

Then xy = 3∗3=9

So the maximum value of xy is 9.

Hence, option 3 is the correct answer.