How to find the difference quotient

Question

4x³-2x

Answer 1

(f(x+h)-f(x))/h

 

= (4(x+h)³-2(x+h)-4x³+2x)/h

 

= (4x³ + 12x²h + 12xh² + 4h³ - 2x - 2h - 4x³ + 2x)/h

 

= (12x²h + 12xh² + 4h³ - 2h)/h

 

= 12x² + 12xh + 4h² - 2