among all the pairs of numbers whose difference is 16 find a pair whose product is as small as possible. what is the minimum product?

Question

anonymous · Answer

maybe -8 and 8 whose product is -64
just a guess though

anonymous · Answer

x-y=16

x=16+y

xy=y(16+y)=16y+y^2
derive:
2y+16=0
y=-8
x=8

amistre64 · Answer

|small| or -small?

anonymous · Answer

$$x-y=16$$
$$x=16+y$$
$$f(x)=xy=x(16+x)$$
now derivative and etc

anonymous · Answer

smallest product -64

anonymous · Answer

y - x = 16
y = x + 16

x(x+16) = x^2 + 16x
vertex is at 8
x = -8
y = 8
minimum product is -64

anonymous · Answer

it just says small

anonymous · Answer

minimum means smallest

anonymous · Answer

i would argue from symmetry, not from calculus.
x - y = 16 or y - x = 16 totally symmetric