Question 800163: solve the non-linear inequality 16x<=x^3
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve the non-linear inequality 16x<=x^3
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x^3-16x >= 0
x(x^2-16) >= 0
x(x-4)(x+4)>= 0
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Draw a number line:: plot x = -4,0,4 on it
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Test a value in each of the resulting 4 intervals::
x(x-4)(x+4)>= 0
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Test x = -10:: -*-*- > 0 ::: false
Test x = -2::: -*-*+ > 0 ::: true, so solutions in [-4,0]
Test x = 2 ::: +*-*+ > - ::: false
Test x = 10::: +*+*+ > 0 ::: true, so solutions in [4,+oo)
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Ans: [-4,0]U[4,+oo)
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Cheers,
Stan H.
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