Question

If x+y=20 then what is the maximum value of 2xy

Answer 1

Answer:

Step-by-step explanation:

Answer: Maximum value of xy = 9

Proof:

Calculus Method:

Given, x+y = 6. Transposing x to RHS,

y = 6 - x

Substituting for y=6 - x,

xy = x(6-x) = 6x - x² = f(x), suppose……………………………………………..(1)

To find the maximum value of xy, we have to find the value of x for which f'(x) = 0 and then check if f(x) is maximum at such a value from the sign of f"(x). If f"(x) is negative (‹ 0) for a particular value of x, it means f(x) is maximum at that value of x.

Differentiating eq.(1) with respect to x,

f'(x) = df/dx = 6–2x

f"(x) = d²y/dx² = -2…………………………………………………………….(2)

Now f'(x) = 0 if 6–2x = 0

i.e. if 2x = 6

i.e. if x = 3

Since, f"(x) is negative (eq.(2)), xy is a maximum and the maximum value of xy is obtained by putting x = 3 in eq.(1).

Maximum of xy = 6x - x² = 6.3 - 3² = 18 - 9 = 9 (Proved)

Just telling method.Not the real answer.