Question

Simplify the difference quotient
[f(2 + h) − f(2)]/h if h ≠ 0.

f(x) = x^2 − 3x

I keep getting the answer wrong...please help.

Answer 1

[f(2 + h) − f(2)]/h if h ≠ 0

if f(x) = x^2 - 3x
f(2+h) = 4+4h+h^2 - 3(2+h)
= h^2 + h - 2
f(2) = 4-6 = -2

[f(2 + h) − f(2)]/h if h ≠ 0.
= (h^2 + h - 2 - (-2))/h
= (h^2 + h)/h
= h + 1