Absolute Maximum?

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1 Answer
Jan 22, 2018

#f_max =5#

Explanation:

#f(x) = x^2-4: x in [-3,0)uu(0,+2]#

Since the domain of #f(x)# is #[-3,0)uu(0,+2]#

Then, #f(x)# is defined for #x in [-3,2]: x!=0#

#f(x)# is a section of parabola with a hole at the point #(0,-4)# which otherwise would have been the absolute mininum.

Since # x^2>0# and increasing over the domain of #f(x)#

#f(x)_max = f(abs(x)_max): x in [-3,0)uu(0,+2]#

#= f(-3) = 3^2-4 =5#