Difference Quotient 2

Question

Let f(x) = -2x-4. Find the difference quotient f(x+h)-f(x)/h. Simplify your answer.

Answer 1

f(x) = -2x-4

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

 

f(x+h) = -2(x+h)-4 = -2x - 2h -4

 

f(x+h) - f(x) = -2x - 2h -4 - (-2x-4)

                   = -2x - 2h -4 + 2x + 4

                   = 2x - 2h = 2(x-h)

 

[f(x+h)-f(x)]/h = [2(x-h)]/h