For the family of functions

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For the family of functions pk(x)=x3−3kx2+9k2xp_k(x)=x^{3}-3kx^{2}+9k^{2}x, determine all real values of kk such that pkp_k has exactly two relative extrema whose xx–coordinates differ by 66.

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