What are the critical numbers of f(x) = 2x^2-x^4?

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What are the critical numbers of f(x) = 2x^2-x^4?

How do you solve this? Thanks.

2007-04-23 05:39:26 · 3 answers · asked by abc 1 in Science & Mathematics ➔ Mathematics

3 answers

critical numbers are when the derivative is equal to zero.

f(x) = 2x^2 - x^4

f ' (x) = 4x - 4x^3

4x - 4x^3 = 0
4x(1 - x^2) = 0
4x(1 - x)(1 + x) = 0

the critical numbers are
x = 0, -1, 1

2007-04-23 05:44:22 · answer #1 · answered by Mathematica 7 · 0⤊ 1⤋

when f(x) = 0

2007-04-23 12:45:23 · answer #2 · answered by Anonymous · 0⤊ 1⤋

f(x) = 2x^2-x^4
=x^2 (2-x^2)=0

x=0

x^2=2
x=sqrt(2)
x= - sqrt(2)

2007-04-23 12:44:29 · answer #3 · answered by iyiogrenci 6 · 1⤊ 0⤋