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Math Help - Find a minimum value

  1. #1
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    Find a minimum value

    Hi all,

    I am stuck at the end of this.

    Find the minimum value of the curve y = x⁴ - 2x + 3 in the domain -3 ≤ x ≤ 3.

    y = x⁴ - 2x + 3
    y’ = 4x - 4x
    stationary points where y’ = 0
    4x - 4x = 0
    4(x - x) = 0
    Stuck here
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  2. #2
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    4(x^3 - x) = 0
    4x(x^2 - 1) = 0

    Can you continue? ^^
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  3. #3
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    Quote Originally Posted by Joel View Post
    Hi all,

    I am stuck at the end of this.

    Find the minimum value of the curve y = x⁴ - 2x + 3 in the domain -3 ≤ x ≤ 3.

    y = x⁴ - 2x + 3
    y’ = 4x - 4x
    stationary points where y’ = 0
    4x - 4x = 0
    4(x - x) = 0
    Stuck here
    Let u= x^2. Then y= x^4- 2x^2+ 3= u^2- 2u+ 3. You can find the minimum value of that by completing the square: u^2- 2u+ 1+ 2= (u- 1)^2+ 2

    The mimimum value of u^2- 2u+ 3 is 2 at u= 1 so the minimum value of x^4- 2x^2+ 3 is __________.
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