Option : (B)
x + y = 8
⇒ y = 8 - x
xy = x(8 - x)
Let f(x) = 8x - x2
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).