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Mathematics 46 Online
OpenStudy (anonymous):

Challenge: If f'(x)=6x^2+3 and f(1)=8 What is f(x)?

OpenStudy (anonymous):

right

OpenStudy (anonymous):

Do you know how to do this

zepdrix (zepdrix):

Is it a challenge? Or just something youwould like assistance with? c:

OpenStudy (anonymous):

no it is a challenge

OpenStudy (anonymous):

What I am meaning is that is what the problem says and I don't know how to solve it

zepdrix (zepdrix):

oh lol

zepdrix (zepdrix):

So to go from \(\large f'\) to \(\large f\) you have to anti-differentiate the function. Do you know how to find the anti derivative of \(\large f'(x)\)?

OpenStudy (anonymous):

no

zepdrix (zepdrix):

Hmm, no? Haven't you learned that yet? You will need that understanding to do this problem. Have you heard of `Integration` maybe? :) You're usually introduced to this topic with the term anti-differentiation, but maybe you've already skipped ahead to integrals.

OpenStudy (anonymous):

wait do you mean this f(x)={6x^2+3dx {6x^2dx+{3dx (6/3x^3)+3x+c 2x^3+3x+c c=-2x^3-3x c=-2(1)^3-3(1) c=-2

zepdrix (zepdrix):

Yes the process looks good. I'm not quite sure about your \(\large c\) though.

OpenStudy (anonymous):

ok so what do I do from here I am stuck

zepdrix (zepdrix):

\[\large f'(x)=6x^2+3\]\[\large f(x)=2x^3+3x+c\] They told us that,\[\large f(1)=8\]So let's plug this in,\[\large 8=2(1)^3+3(1)+c\]

OpenStudy (anonymous):

c=10

zepdrix (zepdrix):

Hmm

zepdrix (zepdrix):

I'm not sure where you're getting 10 from :O I'm coming up with c=3

OpenStudy (anonymous):

I took 8=2(1)^3+3(1)+c 8=2+c 8-2=c c=6

zepdrix (zepdrix):

8=2+3+c

OpenStudy (anonymous):

oh ok I gotcha c=3 so then that is my answer for f(x)=3?

zepdrix (zepdrix):

\[\large \color{orangered}{c=3}\]\[\large f(x)=2x^3+3x+\color{orangered}{c}\] Plug in your c value to establish your final answer for f(x).

OpenStudy (anonymous):

oh ok so the final answer f(x)=2x^3+3x+3

zepdrix (zepdrix):

yay good job!

OpenStudy (anonymous):

ok thanks

zepdrix (zepdrix):

Don't label your problem, "A Challenge". That generally describes some sort of Math Puzzle or Difficult Problem that you've stumbled across. I think that's what the fuss was about at the start of the thread. Just call it a homework problem or something c: heh

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