How to find the local min and max of a piecewise function: do not understand

Question

How did you find the local min and max of a piecewise function? {-x: x<-1 , 2-x^2, x> (or equal to) -1}

Answer 1

In the absence of a concrete example, let me give you a general answer.

Consider each "piece", i.e., each interval of the domain separately.

For each interval, minima and maxima can occur at

- the ends of the interval,

- at points where the function is not differentiable,

- at points where the derivative is 0.

Then you can compare all the above candidates for minima and maxima among all the intervals.