Find the Difference quotient f(x+h)-f(x)/h, where h does not equal zero for the function below

Question

f(x)=2x^2+3x

Simplify the answer as much as possible

 

Thank you

Answer 1

f(x) = 2x² + 3x

f(x+h) = 2(x+h)² + 3(x+h) = 2x² + 4hx +2h² + 3x + 3h

 

(f(x+h)-f(x))/h = (2x² + 4hx + 2h²+3x + 3h - 2x² - 3x)/h = (4hx + 2h² + 3h)/h = h(4x+2h+3)/h = 4x + 2h + 3