Three less than twice another number what is the smallest possible value of their product

Lets assume that x and y are two numbers.

y = 2 x - 3 (3 less than twice another number)

Their product:

x · y = x · (2 x - 3) = 2 x² - 3 x

We find the derivative:

(2 x² - 3 x) ' = 4 x - 3

4 x - 3 = 0

4 x = 3

x = 3/4

y = 2 · 3/4 3 = - 3 / 2

x · y = 3/4 · ( - 3/2) = - 9/8

Answer: The smallest possible value of their product is - 9/8