JEE Advance - Mathematics (1985 - No. 33)
Let $$f\left( x \right) = {\sin ^3}x + \lambda {\sin ^2}x, - {\pi \over 2} < x < {\pi \over 2}.$$ Find the intervals in which $$\lambda $$ should lie in order that $$f(x)$$ has exactly one minimum and exactly one maximum.
\(\lambda \in \left( { - \infty , - {3 \over 2}} \right)\)
\(\lambda \in \left( { - {3 \over 2},0} \right) \cup \left( {0,{3 \over 2}} \right)\)
\(\lambda \in \left( { - {3 \over 2},{3 \over 2}} \right)\)
\(\lambda \in \left( {0,{3 \over 2}} \right)\)
\(\lambda \in \left( { - \infty ,0} \right)\)