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"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 -

    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
    C= 1/2
    check my thinking.

  • Calculus -

    Thank you! That makes sense!

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