Posted by **Stuck** on Saturday, April 3, 2010 at 9:06pm.

"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.

- Calculus -
**bobpursley**, Saturday, April 3, 2010 at 9:11pm
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.

- Calculus -
**Stuck**, Saturday, April 3, 2010 at 9:24pm
Thank you! That makes sense!

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