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10 March, 21:31

What is the local minimum value of the function g (x) = x^4-5x^2+4? (Round answer to the nearest hundredth)

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Answers (2)
  1. 11 March, 01:04
    0
    G (x) = x ^4 - 5 x² + 4

    g ' (x) = 4 x³ - 10 x

    4 x³ - 10 x = 2 x (2 x² - 5) = 0 (the local minimum is where the derivative is equal to zero)

    x = 0,

    2 x² - 5 = 0

    x² = 5/2

    x = + / - √ (5/2) = + / - 1.58

    g (0) = 4 (not the local minimum)

    g (√5/2) = g (-√5/2) = (√5/2) ^4 - 5 (√5/2) ² + 4 =

    = 2.5 ² - 5 · 2.5 + 4 = 6.25 - 12.5 + 4 = - 2.25

    Answer:

    The local minimum is : M ( - 1.58, - 2.25) and N (1.58, - 2.25).
  2. 11 March, 01:14
    0
    The answer is

    g' (x) = 4x^3-10x=0 so (4x-10) x=0 it is x = 0 and x = 5/2

    g (0) = 4

    g (5/2) = x^4-5x^2+4=11.81

    the minimum is M (0, 4)
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