Calculus
posted by Stuck on .
"The line x+y = 0 is tangent to the graph of y = F(x). Find F(x) if F'(x) = x".
I know how to find the antiderivative of F'(x), but I don't know how to use the tangent line to find my constant.

so the line x+y gives a slope of 1
f(x)=1/2 x^2+c but at some x, the tangent line has a slope of 1
f'= x so x=1
what is y when x=1? y=1
so the point of tangency is 1,1
f(x)=1/2 x^2 + C
1=1/2+C
C= 1/2
check my thinking. 
Thank you! That makes sense!