`"Let " f(x) ={underset("log_(1//2) (X +(1)/(2)), 0 lt X lt (3)/(2))underset(lambda , x=0)(x^(2) +x , -1 le X lt0)`.
Discuss global maxima minima for `lambda =0 " and "lambda =1` .

Explanation

To solve the problem, we need to analyze the function \( f(x) \) defined in two segments based on the value of \( x \) and the parameter \( \lambda \). The function is given as:

\[
f(x) =
\begin{cases}
x^2 + x & \text{for } -1 \leq x < 0 \\
\lambda & \text{for } x = 0 \\
\log_{(1/2)}(x + \frac{1}{2}) & \text{for } 0 < x < \frac{3}{2}
...