1. The problem statement, all variables and given/known data Find a function f such that f'(x)=x^3 and the line x+y=0 is tangent to the graph of f. 2. Relevant equations antiderative 3. The attempt at a solution f(x)=(x^4)/4 + C I don't know where to go from here... the tangent line equation is a way to find the slope, no? So rearranging x+y=0 gives y=x which means that the slope is 1....but wait, doesn't y=x mean that the tangent is a straight line, so therefore the derivative is 0? As you can tell, I'm very confused!!