Asked by ken
The solution below corresponds to an inequality involving a quartic function.
Write a possible quartic polynomial inequality that matches the solution. Prove that your inequality matches the solution.
x < 4 and x > 7
Write a possible quartic polynomial inequality that matches the solution. Prove that your inequality matches the solution.
x < 4 and x > 7
Answers
Answered by
Steve
midway between 4 and 7 is 11/2
Since f(x) = x^4 > 0 is satisfied by all x<0 or x>0, just shift that
a simple quartic shifted down would be
x^4 - (11/2)^4 > 0
a more involved one shifted right is
(x - 11/2)^4 > 0
16x^4 - 352x^3 + 2904x^2 - 10648x + 14641 > 0
Since f(x) = x^4 > 0 is satisfied by all x<0 or x>0, just shift that
a simple quartic shifted down would be
x^4 - (11/2)^4 > 0
a more involved one shifted right is
(x - 11/2)^4 > 0
16x^4 - 352x^3 + 2904x^2 - 10648x + 14641 > 0
Answered by
ken
how did u get 11/2
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