Question

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

Answer 1

right

Answer 2

Do you know how to do this

Answer 3

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

Answer 4

no it is a challenge

Answer 5

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

Answer 6

oh lol

Answer 7

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 \(\large f'(x)\)?

Answer 8

no

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

ok so what do I do from here I am stuck

Answer 13

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

Answer 14

c=10

Answer 15

Hmm

Answer 16

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

Answer 17

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

Answer 18

8=2+3+c

Answer 19

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

Answer 20

\[\large \color{orangered}{c=3}\]\[\large f(x)=2x^3+3x+\color{orangered}{c}\]

Plug in your c value to establish your final answer for f(x).

Answer 21

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

Answer 22

yay good job!

Answer 23

ok thanks

Answer 24

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