How to find the domain and range of #3x^4 -4 x^3 # ?

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#3x^4 -4 x^3 #

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Answer 1 · 2018-04-19T11:24:18

See below.

This is a polynomial so it is defined for all #x#. Hence domain is:

#{x in RR }#

The first term is of greater degree than the second term and its exponent is even. This means that it is always #>=0#.

The minimum value of the function is consequently #0#:

as #x->+-oo color(white)(888888)# #3x^4-4x^3->oo#

#{y in RR |0 <= y < oo}#

This is verified by its graph.

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