College Algebra (10th Edition)

$\displaystyle 2x+h-1$
We are given: $f(x)=x^{2}-x+4$ We find the difference quotient: $\displaystyle \frac{f(x+h)-f(x)}{h}$ $\displaystyle =\frac{(x+h)^{2}-(x+h)+4-(x^{2}-x+4)}{h}$ $\displaystyle =\frac{x^{2}+2xh+h^{2}-x-h+4-x^{2}+x-4}{h}$ $\displaystyle =\frac{2xh+h^{2}-h}{h}$ $\displaystyle =\frac{h(2x+h-1)}{h}$ $\displaystyle =2x+h-1$