Question

find the difference quotient
 2x^2-x+3y=2y

Answer 1

We need to express y in terms of x first:

2x²-x+3y=2y, so y=x-2x², which can be written y(x)=x-2x².

The difference quotient Δ is (y(x+h)-y(x))/h:

Δ=(x+h-2(x²+2hx+h²)-x+2x²)/h=

(x+h-2x²-4hx-2h²-x+2x²)/h=1-4x-2h⇒1-4x as h→0, when 1-4x is known as the derivative of y(x).