Respuesta :

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f(x)=x(x-36)=x²-36x

f'(x) = 2x-36 =0. implies x = 18

answer is 18 and -18
fichoh

The two numbers whose which differs by 36 and gives a minimum value for the product is - 18 and 18

Let the first number = a

The second number = a + 36

Product of the two numbers :

a(a + 36)

a² + 36a

At the minimum point ; da/dx = 0

dy/dx= 2a + 36

2a + 36 = 0

2a = - 36

a = - 36 / 2

a = - 18

Hence,

a + 36

-18 + 36 = 18

Therefore, the two numbers are - 18 and 18

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