How do you find the local extrema for #F(x)= sin (x + (π/2) )#?
Local extrema are where the first derivative of the expression is equal to zero.
The first derivative of an expression is an inflection point of the expression wherever it is equal to zero. It is a local maxima or minima (extrema) depending on whether the second derivative is positive or negative. IF the second derivative changes sign, then the point is an inflection point and not an extrema.
This can also be determined from the change in sign of the first derivative around the point.