Let `f(x)=2sin^(3)x+lamdasin^(2)x,-(pi)/2ltxlt(pi)/2`. If `f(x)` has exactly one minimum and one maximum, then `lamda` cannot be equal to

Options

A. 1
B. 0
C. 3
D. 4

Explanation

To solve the problem, we need to analyze the function \( f(x) = 2\sin^3 x + \lambda \sin^2 x \) and determine the conditions under which it has exactly one minimum and one maximum.

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

We start by differentiating \( f(x) \):

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