Question

f(x) = x^2 + x+1 compute the ratio
f(x+h) - f(x)/h
can someone show me the steps for this one its really confusing me.

Answer 1

is it limit ?

Answer 2

no no I just started learning this stuff theres no limit things and higher stuff involved

Answer 3

First solve for f(x+h): (x+h)^2 + (x+h) + 1
Then plug it into that second part, the formula:
[(x+h)(x+h)+x+h+1-(x^2+x+1)]/h

Answer 4

Now foil it out and distribute the negative:
[x^2 + 2xh + h^2 + x + h + 1 - x^2 -x -1]/h
Combine like terms:
[2xh + h^2 + h]/h

Answer 5

Pull out the h:
[h(2x+h+1)]/h
Reduce:
2x+h+1

Answer 6

And that's the derivative. Were you given x=something?

Answer 7

no I dont think so.

Answer 8

Ok, then I think that's it.

Answer 9

thats the whole problem that I wrote up there. I dont understand how u plug in x^2+x+1 into the f(x+h) part

Answer 10

it is derivative, but it a long method

Answer 11

sowwy...and p->q all you do is just plug in (x+h) for every instance of x.

Answer 12

I thought it was the otherway around like whatever they say let f of x is u plug that into the problem they gave u

Answer 13

OOO wait I got it it just clicked. What you said is basically like f(1)

Answer 14

cool cool ty ty

Answer 15

winterfez can you explain the shortcut?