Mathematics

Problem

Let the curve be defined by

x^{3}+y^{3}+3kxy=25

. The curve contains the point with

x

–coordinate

2

. For what value of

k

does the tangent line at that point become horizontal? a)

\dfrac{4}{\sqrt[3]{41}}

-\dfrac{2}{\sqrt[3]{41}}

-\dfrac{4}{\sqrt[3]{41}}

-\dfrac{4}{3\sqrt[3]{41}}