6) given f(x)=x² - 4x determine the following: (f(x+h)-f(x))/h

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$: $f(x + h)=(x + h)^2-4(x + h)=x^{2}+2xh+h^{2}-4x - 4h$

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

$f(x + h)-f(x)=(x^{2}+2xh+h^{2}-4x - 4h)-(x^{2}-4x)$ $=x^{2}+2xh+h^{2}-4x - 4h - x^{2}+4x=2xh+h^{2}-4h$

Step3: Find $\frac{f(x + h)-f(x)}{h}$

$\frac{f(x + h)-f(x)}{h}=\frac{2xh+h^{2}-4h}{h}$ Factor out $h$ from the numerator: $\frac{h(2x + h-4)}{h}=2x+h - 4$

Answer:

$2x+h - 4$