Answer to Question #17669 in Calculus for hsd

Question

Find the absolute and local maximum and minimum values of f(x)={x^2 −1≤x<0
{2−x^2 0≤x≤1.
If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.

Absolute maxima
x = y =
x = y =
x = y =

Absolute minima
x = y =
x = y =
x = y =

Local maxima
x = y =
x = y =
x = y =

Local minima
x = y =
x = y =
x = y =

Answer 1

we must find f'
f'=2x when -1<x<0
f'=-2x when 0<x<1
f'=0 x=0

to find absolute maxima and minima we must find values atthe ends, at points of discontinuity and at points where f'=0
x=0 f=2
x=-1 f=0
x=1 f=1
and when x<0 and x->0 we have that f->-1 soabsolute maxima x=0 y=f(x)=2 absolute minima does not exist x->0 we have that f->-1 local minimax=-1 f=0, x=1 f=1 local maxima x=0 y=f(x)=2