Math Help - Primitive Functions

At all points on a certan curve, y'' = 2x. The point (3,6) belongs to the curve and its tangent at this point is inclined at 45 degrees to the X-axis. Find the equation of the curve.

How exactly do I use the bold part for this problem? I've found y' = x^2 + c...

Oh, and is the answer actually y = x^2 - 5x + 12 (txtbk answer) cause it doesn't look right to me.

Originally Posted by xwrathbringerx

At all points on a certan curve, y'' = 2x. The point (3,6) belongs to the curve and its tangent at this point is inclined at 45 degrees to the X-axis. Find the equation of the curve.

How exactly do I use the bold part for this problem? I've found y' = x^2 + c...

Oh, and is the answer actually y = x^2 - 5x + 12 (txtbk answer) cause it doesn't look right to me.

The bolded part informs you that .

So this is a differential equation with and

I'm sure you can proceed from here.