Please help me to answer this, thank you!

Find the equation of the curve that satisfies the differential equationf"(x) = 6x - 12 and which passes through the points (0, -8) and (1, -1).

- May 17th 2006, 01:33 AMLilDragonflyUse integral calculus to solve differential equation problems
Please help me to answer this, thank you!

Find the equation of the curve that satisfies the differential equation*f"*(*x*) = 6x - 12 and which passes through the points (0, -8) and (1, -1). - May 17th 2006, 04:27 AMtopsquarkQuote:

Originally Posted by**LilDragonfly**

Sooooo:

$\displaystyle f(0)=-8 = 0^3-6*0^2+a*0+b=b$

Thus b = -8.

$\displaystyle f(1)=-1=(1)^3-6(1)^2+a(1)-8$

gives:

$\displaystyle -1=1-6+a-8=-13-a$

or

$\displaystyle a = 12$

-Dan - May 17th 2006, 05:33 AMThePerfectHacker
I do not know if you understood what topsquak said, but when you have,

$\displaystyle f''(x)=6x-12$

It means if you integrate both sides you have,

$\displaystyle f'(x)=3x^2-12x+a$ with some constant $\displaystyle a$,

the reason to why f''(x) becomes f'(x) is because when you integrate a derivative of a function you get back the function (definition of integral). So when you have f''(x) integrating once would yield f'(x) so you need one more time:

$\displaystyle f(x)=x^3-6x^2+ax+b$

Then use topsqaurk post to complete the problem.