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What are the absolute extrema of # f(x)= 2 + x^2 in [-2, 3]#?

1 Answer

Alan N. · Anjali G

Mar 5, 2017

#f(x)# has an absolute minimum of 2 at #x=0#

Explanation:

#f(x)= 2+x^2#

#f(x)# is a parabola with a single absolute minimum where #f'(x)=0#

#f'(x) =0+2x = 0 -> x=0#

#:.f_min(x) = f(0) = 2#

This can be seen on the graph of #f(x)# below:

graph{2+x^2 [-9.19, 8.59, -0.97, 7.926]}

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