Let `f(x)=sin^3x+lambda sin^2x , -pi/2 < x < pi/2` Find the intervals in which `lambda` should lie in order that `f(x)` has exactly one minimum and exactly one maximum.

Explanation

To solve the problem, we need to analyze the function \( f(x) = \sin^3 x + \lambda \sin^2 x \) and determine the conditions on \( \lambda \) such that \( f(x) \) has exactly one minimum and one maximum in the interval \( -\frac{\pi}{2} < x < \frac{\pi}{2} \).

### Step 1: Find the derivative of \( f(x) \)

To find the critical points where the maximum and minimum can occur, we first need to compute the derivative \( f'(x) \).

\[
f'(x) = \frac{d}{dx}(\sin^3 x) + \lambda \frac{d}{dx}(\sin^2 x)
...