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Home Q & A Board Science-Related Homework Help Mathematics Calculus
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slimes slimes
wrote...
Posts: 162
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3 years ago
What did I do wrong here??
h->0 f(x + h) - f(x)/h
h->0 6(x + h)^3 - 9 (x + h) + 4 - (6x^3 - 9x + 4)
h-> 6x^3 + 18x^2h + 18h^2x + 6h^2 - 9x - 9h + 4 - 6x^3 + 9x - 4/h
h->0 18x^2h + 18h^2x + 6h^2/h = 6h(3hx + 3x^2 + h)/h
                                                           = 18xh + 18x^2 + 6h <- Unsure of what to do around here
ANSWER: f^1(x) = 18x^2 - 9
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wrote...
#1
Educator
3 years ago
Hi slimes
slimes Author
wrote...
#2
3 years ago
Do you have to spilt it into 2 derivatives? It's similar to a question I have done before https://biology-forums.com/index.php?topic=1973769.msg5161397#msg5161397 c)
Is it because of the ^3?
wrote...
#3
Educator
3 years ago
It's like (c) from that topic. You don't need to split the terms, but I just find it easier to do two separate terms then all of the combined. I don't think there's a rule that says you're not allowed.
slimes Author
wrote...
#4
3 years ago
shouldn't the 6(x + h)^3 -> x^3 + 2x^2h + 2xh^2 + h^2x + h^3?
At the part (x^2 + 2xh + h^2)(x + h) you multiplied each term with x and h? That's what I did.
= x^3 + x^2h + 2x^2h + 2xh^2 + h^2x + h^3
= Answer: x^3 + 2x^2h + 2xh^2 + h^2x + h^3
wrote...
#5
Educator
3 years ago
You forgot to multiply by the factor 6
slimes Author
wrote...
#6
3 years ago Edited: 3 years ago, slimes
ended up getting 6x^3 + 12x^2h + 12xh^2 + 6h^2 + 6h^3, which is not the same as your answer
Post Merge: 3 years ago

Plus before multiplying the 6 you got x^3 + 3hx^2 + 3h^2x + h^3
wrote...
#7
Educator
3 years ago
Look @ the top right corner of my solution, I show you the correct way to expand (x+h)^3.

So you're not happy with my solution? Is there something you don't understand about the steps I showed? I don't get the issue...
slimes Author
wrote...
#8
3 years ago Edited: 3 years ago, slimes
No I did not say that I was just confused about something but found out that I was missing something after looking at your solution
Thanks
Post Merge: 3 years ago

bio man I was given a question and part of it is where I had to factor 2(t + h)^4
Would this be correct?
(t+h)(t+h)(t+h)(t+h)
= (t^2 + th + th + h^2 + t^2 + th + th + h^2)
= 2(2t^2 + 4th + 2h^2)
= 4t^2 + 8th + 4h^2
When I inserted 2(t + h)^4 in a factoring calculator machine, the answer was 2h^4 +8h^3t + 12h^2t^2 + 8ht^3 + 2t^4? I did all the steps. Where did I go wrong?
wrote...
#9
Educator
3 years ago
It would be something like this:
slimes Author
wrote...
#10
3 years ago
thanks can I actually post this question? It was sort of difficult because there was a lot of terms and even though I got all of the factoring right. The last step to completing the problem which was factoring the equation after canceling everything out, turned out to be un factorable and I didnt know what do when that had happened. I can show you what I did.
wrote...
#11
Educator
3 years ago
Yes, start a new topic, will look at it
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