Question

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?

Answer 1

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

Answer 2

x-y=16

x=16+y

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

Answer 3

|small| or -small?

Answer 4

\[x-y=16\]
\[x=16+y\]
\[f(x)=xy=x(16+x)\]
now derivative and etc

Answer 5

smallest product -64

Answer 6

y - x = 16
y = x + 16

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

Answer 7

it just says small

Answer 8

minimum means smallest

Answer 9

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