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Math Help - Problem (Differentiation)

  1. #1
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    Exclamation Problem (Differentiation)

    (i) Show that (x - 1) is a factor of x^3 - 4x^2 +4x - 1 and hence find the other factors.

    (ii) Hence or otherwise find the maximum and the minimum points of the function f(x) = 2x^(5/2) +5x^2 - 5x +1.

    I managed to work out part (i) but I can't see how I can use part(i) to solve part (ii). I am not noticing any relationship between them.

    NO IDEA

    Thanks in advance for any help.
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  2. #2
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    Quote Originally Posted by yobacul View Post
    (i) Show that (x - 1) is a factor of x^3 - 4x^2 +4x - 1 and hence find the other factors.

    (ii) Hence or otherwise find the maximum and the minimum points of the function f(x) = 2x^(5/2) +5x^2 - 5x +1.

    I managed to work out part (i) but I can't see how I can use part(i) to solve part (ii). I am not noticing any relationship between them.
    To calculate the extrema of f you need the first derivation first:

    f'(x)=5x^{\frac32} +10x - 5

    Solve the equation f'(x) = 0 for x:

    5x^{\frac32} +10x - 5 = 0

    Use the substitution u = x^{\frac12}~\implies~x = u^2 . The equation becomes:

    5u^3 +10u^2 - 5=0~\implies~u^3+2u-1=0

    Now use the same method to solve this equation as you have done with the first one. Obviously one solution is u = -1. Now calculate the other solutions. Re-substitute to get the values of x.
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