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