# Splitting cases

Calculus Level 3

$\large f(x) = \sin^3(x) + k \sin^2(x)$

For variable $$k$$ independent of $$x$$, consider the function $$f$$ on the interval $$-\frac\pi2 < x < \frac\pi2$$ as described above. Find the sum of all integral values of $$k$$ such that $$f(x)$$ has exactly one minimum value and one maximum value.

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