**Option : (B)**

x + y = 8

⇒ y = 8 - x

xy = x(8 - x)

Let f(x) = 8x - x^{2}

**Differentiating f(x) with respect to x, we get **

f’(x) = 8 - 2x

**Differentiating f’(x) with respect to x, we get **

f’’(x) = -2 < 0

**For maxima at x = c, **

f’(c) = 0 and f’’(c) < 0

f’(x) = 0 ⇒ x = 4

**Also,**

f’’(4) = -2 < 0

**Hence,**

x = 4 is a point of maxima for f(x) and

f(4) = 16 is the maximum value of f(x).