Answer:
- f(x+h) = (2x² -x +2) +4xh -h +2h²
- (f(x+h) -f(x))/h = 4x -1 +2h
Step-by-step explanation:
Like a lot of algebraic manipulation associated with average rate of change, it is not difficult, but it can be tedious.
a)
[tex]f(x+h)=2(x+h)^2-(x+h) +2 = 2(x^2 +2xh +h^2)-x -h +2\\\\\boxed{f(x+h)=2x^2-x+2+4xh-h+2h^2}[/tex]
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b)
Then the difference quotient is ...
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(2x^2-x+2)+4xh-h+2h^2-(2x^2-x+2)}{h}\\\\=\dfrac{4xh-h+2h^2}{h}\\\\\boxed{\dfrac{f(x+h)-f(x)}{h}=4x-1+2h}[/tex]
