`"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` . For what values of `lambda` does f(x) has global maxima.

Explanation

Graph of `y=f(x) " for " lambda =0`

No global maxima minima
Graph of `y= f(x) " for " lambda =1`

Global maxima is 1, which occurs at x=0
Global minima does not exists
`underset( x to0)("Lim") f(x) =0 , underset(x to0)("Lim") f(x) =1, f(0) =lambda`
For global maxima t exists
`f(0) le 1" "rArr " " lambda ge1.`