Solution to #3 on Winter Break Review Packet

Find and simplify the difference quotient of f(x) = (2x+1)^2.

We know that the formula for the difference quotient is (f(x+h)-f(x))/h, so we just plug in numbers to get the answer.

(f(x+h)-f(x))/h
((2(x+h)+1)^2)-(2x+1)^2)/h
((4x^2+8h*x+4x+4h^2+4h+1)-(4x^2+4x+1))/h
(8h*x+4h^2+4h)/h
4(2x+h+1)
8x+4h+1