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domain and range of this function?
x^4 -4x^2 -2
and the critical points please
1 Answer
- ?Lv 69 years ago
to find the critical points:
take the derivative and set equal to zero
4x^3 - 8x = 0
x(4x^2 - 8) = 0
4x^2 - 8 = 0
4x^2 = 8
x^2 = 2
x = sqrt(2)
so critical points are at x = 0, +/- sqrt(2)
plugging these back into the original equation gives:
0^4 - 4(0^2) - 2 = -2
(0, -2)
sqrt(2)^4 - 4(sqrt(2)^2) - 2
4 - 8 - 2 = -6
(+/- sqrt(2), -6)
so the domain is all real numbers and the range is (-6, infinity)
Hope this helps.
