What are the extrema of #f(x) = 64-x^2# on the interval #[-8,0]#?

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Answer 1 · 2015-12-30T04:22:16

Find the critical values on the interval (when #f'(c)=0# or does not exist).

#f(x)=64-x^2#

#f'(x)=-2x#

Set #f'(x)=0#.

#-2x=0#

#x=0#

And #f'(x)# is always defined.

To find the extrema, plug in the endpoints and the critical values. Notice that #0# fits both of these criteria.

#f(-8)=0larr"absolute minimum"#

#f(0)=64larr"absolute maximum"#

graph{64-x^2 [-8, 0, -2, 66]}