Question

f(x)=2x^2+x

if you plug in (x+h) for all the X's
will you get 3x^2+3h^2+4xh

Answer 1

there is no 3 in it

Answer 2

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

Answer 3

Right but when i did that i distributed first (x+h)(x+h) and got x^2+xh+xh+h^2

Answer 4

when you multiply out you get
\[2(x+h)(x+h)+x+h=2(x^2+2xh+h^2)+x+h\]
\[=2x^2+4xh+2h^2+x+h\] there are not like terms to combine here

Answer 5

i think i see what you did
you added \(2h^2+h\) and got \(3h^2\) but they are not like terms, because one is a square and the other isn't
so you cannot add them in to one term

Answer 6

oh okay okay so after that i have to (2x2+4xh+2h2+x+h)-(2x^2+2) over h
I have no clue how to complete it

Answer 7

now you have like terms

Answer 8

i assume it is actually
\[\frac{f(x+h)-f(x)}{h}\] am i right?

Answer 9

yes

Answer 10

then you had a typo there
you wrote \[(2x^2+4xh+2h2+x+h)-(2x^2+2)\] but it should be \[(2x2+4xh+2h2+x+h)-(2x^2+x)\]

Answer 11

i.e. the \(x\) instead of a \(2\) at the end

Answer 12

oh yea Once i simplify i gotten 4xh+2h^2+h correct?

Answer 13

\[(2x2+4xh+2h2+x+h)-(2x^2+x)\]distribute the minus sign and get \[2x^2+4xh+2h2+x+h-2x^2-x\]

Answer 14

you are right, yes

Answer 15

\[4xh+2h^2+h\] is correct for the numerator yes

Answer 16

so how am i suppose to divide 4xh/h

Answer 17

cancel an \(h\) from each term, or factor out the common factor of \(h\) in the numerator and cancel all at once

Answer 18

\[\frac{4xh}{h}=\frac{4x\cancel h}{\cancel h}=4x\] for example

Answer 19

or you can write
\[\frac{4xh+2h^2+h}{h}=\frac{h(4x+2h+1)}{h}\] then cancel
looks better that way probablyl

Answer 20

so i should end up with 4x+h^2 right

Answer 21

no

Answer 22

is this step clear? factoring out an \(h\) in the numerator?\[\frac{4xh+2h^2+h}{h}=\frac{h(4x+2h+1)}{h}\]

Answer 23

okay i dont under stand so after i factor it out then what

Answer 24

cancel the \(h\)

Answer 25

\[\frac{4xh+2h^2+h}{h}=\frac{h(4x+2h+1)}{h}=\frac{\cancel h(4x+2h+1)}{\cancel h}=4x+2h+1\]

Answer 26

thank you soooooooo much!