Question

PLEASE HELP URGENT!!! Cannot figure this out, due tonight.

Answer 1

• f(x+h) = (2x² -x +2) +4xh -h +2h²
• (f(x+h) -f(x))/h = 4x -1 +2h

Explanation:

Like a lot of algebraic manipulation associated with average rate of change, it is not difficult, but it can be tedious.

a)

`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}`

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b)

Then the difference quotient is ...

`(f(x+h)-f(x))/(h)=((2x^2-x+2)+4xh-h+2h^2-(2x^2-x+2))/(h)\\\\=(4xh-h+2h^2)/(h)\\\\\boxed{(f(x+h)-f(x))/(h)=4x-1+2h}`