Find f. Use C for the constant of the first derivative and D for the constant of the second derivative.
f '' (x)=24x^3 -18x^2+ 8x

Question

Find f. Use C for the constant of the first derivative and D for the constant of the second derivative.
f '' (x)=24x^3 -18x^2+ 8x

loser66 · Answer

is it not take integral 2 times?

anonymous · Answer

i think you have to take the anti-derivative twice

loser66 · Answer

the same! antiderivative = integral

anonymous · Answer

got it  still very cofused  can either of you help

anonymous · Answer

would you mind trying the problem

anonymous · Answer

Using Mathematica 8, the solution to the following differential equation$$f''(x)=24 x^3-18 x^2+8 x $$is$$f(x)=c_2 x+c_1+\frac{6 x^5}{5}-\frac{3 x^4}{2}+\frac{4 x^3}{3} $$

anonymous · Answer

i got 6x^5/5 -3x^4/2 +4x^2 +Cx+D

espex · Answer

@alexthomas it looks like you didn't take the integral of your $4x^2$ term for the second time to get the $\frac{4}{3}x^3$ before your Cx+D.

anonymous · Answer

$$f"\left( x \right)=24x ^{3}-18x ^{2}+8x$$
$$f \prime \left( x \right)=\frac{ 24x ^{4} }{ 4 }-\frac{ 18x ^{3} }{ 3 }+\frac{ 8x ^{2} }{ 2  }+c$$
f'(x)=6x^4-6x^3+4x^2+c
similarly you can find f(x)