Here is the question:

Find a functionfwhich satisfies both of the following properties:

f ' (x) = x^3

The line x + y = 0 is tangent to the graph of f.

I figured out that f(x) is 1/4x^4 + C. Now I don't know what to do. I know I need to figure out C but i'm stuck. I isolated x+y=0 for y to get y= -x, and the derivative of that is -1, so the slope of the tangent line is -1. I don't know if im supposed to do this or how to relate this to C. Please help!