calculus/double integral?

[roadrunner]

Here's one I'm stumped on:

At every point of a certain curve y'' = -3. Find the equation of this curve if it passes through the origin and has the slope 1 at that point.

Will integrated twice help me?

 

[roadrunner]

Oops - will integrating twice help me?

 

[tkhunny]

y'' = -3
y' = -3x + C

We are given: "has the slope 1 at [the Origin]."

1 = -3(0) + C ==> C = 1
y' = -3x + 1

Do it again for the next chunk of information.

 

[roadrunner]

Ok, so I come up with

y= -3xsquared/2 + x