Let the curve be defined by

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

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}}

(b)

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

(c)

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

(d)

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