Question

2.7
score: 21/25 answered: 21/25
question 22
find the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$, for the given function $f$.
f(x)=2x^{2}-x
question help: video ebook written

Explanation:

Step1: Find $f(x + h)$

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

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

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

Step3: Find the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{4xh+2h^{2}-h}{h}=\frac{h(4x + 2h-1)}{h}=4x + 2h-1$

Answer:

$4x + 2h-1$