Sarthaks Test
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If x + y = 8, then the maximum value of xy is :

A. 8 

B. 16 

C. 20 

D. 24

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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).

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