Question

find the difference quotient, [f(X+h)-f(x)]/h, for the function and simplify it.
P(X)=-10x^3+2

Answer 1

I guess P=f

Answer 2

do you know how to find P(x+h)?

Answer 3

P(x)=-10x^3+2
so to find P(x+h)
you replace the x's in P(x)=-10x^3+2 with (x+h)'

Answer 4

ok

Answer 5

so what is P(x+h)=?

Answer 6

p(x+h)

Answer 7

what is that equal to given p(x)=-10x^3+h

Answer 8

oops p(x)=-10x^3+2*

Answer 9

\[\text{ if } P(x)=-10x^3+2 \text{ then } \\ P(fish)=-10(fish)^3+2 \\ \text{ so } P(x+h)=?\]

Answer 10

should i expand (X+h)^3

Answer 11

eventually need to simplify*

Answer 12

but do you think you know what P(x+h) is
and if so what is it

Answer 13

im at [(-10x-10)^3+10x^3-2]/h

Answer 14

thats -10(x+h)^3

Answer 15

well P(x+h) isn't -10(x+h)^3
but it is -10(x+h)^3+2
remember P(x)=-10x^3+2

Answer 16

\[\frac{p(x+h)-p(x)}{h} \\ =\frac{[-10(x+h)^3+2]-[-10x^3+2]}{h}\]

Answer 17

haha yup still doesnt dodisturb:)

Answer 18

no distribute the minus sign in front of the second grouping there

Answer 19

you will see something cancel after distributing the minus in front of the second grouping

Answer 20

\[\frac{p(x+h)-p(x)}{h} \\ =\frac{[-10(x+h)^3+2] \color{red}{-}[-10x^3+2]}{h}\]
see that red - in front of the [ ]

Answer 21

-(a+b)=-a-b

Answer 22

it changes the sign of the terms inside the [ ]

Answer 23

yes i know lolololol

Answer 24

do you see something cancel then?

Answer 25

how would i simplify it

Answer 26

yea the 2 lol i told you it didnt matter lol

Answer 27

well that 2 does matter from the p(x+h)
so it cancel with the 2 from the p(x)

Answer 28

if you don't see that p(x+h)=-10(x+h)^3+2
then both the 2's would have not cancel

Answer 29

can just like finish the problem ill analyze it your too good of a teacher:) or at least tell me what to do with the (x+h)^3

Answer 30

do i have to expand it????

Answer 31

\[\frac{p(x+h)-p(x)}{h} \\ =\frac{[-10(x+h)^3+2]-[-10x^3+2]}{h} = \frac{-10(x+h)^3+2+10x^3-2}{h}\]
now you cancel the 2's
and as suggested earlier by you need to exapnd the (x+h)^3

Answer 32

after you expand the (x+h)^3
you will see another pair cancel

Answer 33

what do you have after doing that?

Answer 34

[-10x^2-10h^3-30x^2h-30xh^2+10x^2]/h

Answer 35

im lost

Answer 36

sorry this is the part ive been stuck on since the beggining

Answer 37

\[(x+h)^3=x^3+3x^2h+3xh^2+h^3 \\ -10(x+h)^3=-10x^3-30x^2h-30xh^2-10h^3 \]
when did you get -10x^2 +10x^2 ?

Answer 38

\[\frac{p(x+h)-p(x)}{h} \\ =\frac{[-10(x+h)^3+2]-[-10x^3+2]}{h} = \frac{-10(x+h)^3+2+10x^3-2}{h} \\ \frac{-10x^3-30x^2h-30xh^2-10h^3+10x^3}{h}\]
you should see that -10x^3+10x^3=?

Answer 39

cancell

Answer 40

yes
not the remaining terms on top have an h
and there is also a h on bottom

Answer 41

so i will let you decide what do we need to do next

Answer 42

now*

Answer 43

factor it out

Answer 44

yes factor a h on top
and then cancel that h with the h on bottom
since h/h=1

Answer 45

thank you<333