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How do you find the local extrema for #f(x) = (x-3)^3# on (-∞, ∞)?

1 Answer

Nov 11, 2016

#f# has no local extrema.

Explanation:

#f'(x) = 3(x-3)^2# is never undefined and is #0# only at #0#, so the only critical number is #0#.

#f'(x)# is always positive for #x != 0#, so #f# is increasing on #(-oo,oo)#.

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