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Find a function f which 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. So I then figured out what x value causes x^3 to also be -1, and it turns out to be -1. This is the x-coordinate at which the line is tangent to. So the y coordinate would be -1 + y=0. So y is 1. The point at which the line is tangent to f is (-1,1). If everything up to this point is correct, how do I find C?

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# Homework Help: Anti Derivative Question

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