Find an equation of a curve that intersects at right angles every curve of the family y=1/x+k (where k takes all real values)? Answer: y=(1/3)x^3 12/26/2013 | Sun from Los Angeles, CA | 1 Answer | 0 Votes Mark favorite Subscribe Comment
f(x) = 1/(x + k) f'(x) = -1/ (X + k)^{2} g(x) =the function which is perpendicular to f(x) g^{'} ( X) = -1/ f'(x) = -1 / ( -1/ x +k)^{2}= (X +k) ^{ 2} g(x) = ∫ ( X + k) ^2) dx = 1/3 ( X + k ) ^{3} + C 12/26/2013 | Parviz F. Comment Comments It's not 1/(x+k), it's 1/x+k. 12/27/2013 | Sun from Los Angeles, CA Thanks. I've got it. 12/27/2013 | Sun from Los Angeles, CA Comment
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