Question

"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.

Answer 1

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.

Answer 2

Thank you! That makes sense!