Solving Function Given Tangent Line: x+y=0

[fk378]

Homework Statement

Find a function f such that f'(x)=x^3 and the line x+y=0 is tangent to the graph of f.

Homework Equations

Need antiderivative

The Attempt at a Solution

I found the antiderivative, aka the function, to be (x^4)/4 + C
Since the tangent like is x+y=0, --> y=-x, so the slope is -1
If the slope is -1, that means the derivative, x^3 also equals -1
Plugging in f(-1) gives 1/4 + C

Now I don't know what to do with that.

 

[Saladsamurai]

It is saying that the tangent to f is -1, not f itself.

Casey

 

[fk378]

It is saying that the tangent to f is -1, not f itself.

Casey

Well wouldn't it still be the same slope anyhow?

 

[HallsofIvy]

Where (what x) is the slope of x⁴/4+ C equal to -1? If x+ y= 0 is tangent to y= x⁴/4+ C they must have the same y value there.