find the difference quotient of f; that is, find (f(x + h)-f(x))/h, h≠0, for the following function…

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x): [ \begin{align*} f(x + h)&=(x + h)^2-4(x + h)+4\ &=x^{2}+2xh+h^{2}-4x-4h + 4 \end{align*} ]

Step2: Calculate f(x + h) - f(x)

[ \begin{align*} f(x + h)-f(x)&=(x^{2}+2xh+h^{2}-4x-4h + 4)-(x^{2}-4x + 4)\ &=x^{2}+2xh+h^{2}-4x-4h + 4-x^{2}+4x - 4\ &=2xh+h^{2}-4h \end{align*} ]

Step3: Find the difference quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}-4h}{h}\ &=\frac{h(2x + h-4)}{h}\ &=2x+h - 4 \end{align*} ]

Answer:

$2x+h - 4$