Question

Please help, Evaluate: if f(x)=2x-x^2, what is f(x+h)-f(x)/h

Answer 1

\[f(x+h)=2(x+h)-(x+h)^2\] is a start

Answer 2

multiply it out, combine like terms

Answer 3

Where does the -(x+h)^2 come from?

Answer 4

\[ f(x)=2x-x^2\]
\[ f(\spadesuit)=2\spadesuit-\spadesuit^2\]\[ f(\heartsuit)=2\heartsuit-\heartsuit^2\]\[ f(\diamondsuit)=2\diamondsuit-\diamondsuit^2\]\[\\f(\clubsuit)=2\clubsuit-\clubsuit^2\]

Answer 5

\[f(x+h)=2(x+h)-(x+h)^2\]

Answer 6

it is algebra from here on in

Answer 7

substitute (x+h) for x when calculating f(x+h)

Answer 8

Ok, so you're essentially plugging x+h into every x of the equation 2x-x^2?

Answer 9

yes

Answer 10

Alright, so I get 2(x+h)-(x+h)^2-(2x-x^2) for the top, then I multiply out -(x+h)^2 to get -(x^2+2hx+h^2)?

Answer 11

you should not be getting x^2 term after the subtraction. Please check your simplification step.

Answer 12

\[2x + 2h - x^2 - 2hx - h^2 -2x + x^2 = 2h - 2hx\]

Answer 13

Now you can divide it by h to get the answer

Answer 14

so now 2h-2hx/h ?