Let the number be .
The cube of a number exceed four times its square means .
Now solve the inequality is .
Rewrite the inequality as .
The function .
First solve the equation .
To find the solution of the inequality , use the intervals
,
and
.
Interval | \Number chosen | \value of ![]() | \
Conclusion | \
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Negative | \
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Negative | \
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Positive | \
From the above table, conclude that for all numbers
for which
.
Thus, the solution set is .
Therefore, the solution of is
or in interval notation
.
;
.