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c2 differentiation

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  1. Offline

    ReputationRep:
    given that  y= x^\frac{3}{2} + \frac{48}{x}

    find the value of x and the value of y when dy/dx = 0

    ok, so i've found dy/dx to be  \frac{3}{2}x^\frac{1}{2} - \frac{48}{x^2}

    but i'm having trouble evaluating for dy/dx = 0.

    I get to  x^\frac{5}{2} = 32 but am unsure of how to solve this. (also have i multiplied through by x^2 properly?)
  2. Offline

    ReputationRep:
    Raise both sides to the power 2/5 .

    EDIT: And yeah your rearranging and multiplication of x^2 is fine.
  3. Offline

    ReputationRep:
    i get x = 4, is that correct?
  4. Offline

    ReputationRep:
    You know from rules of indices that x^5/2 is the square root of x to the power of 5 so take the 5th root of 32 and you have the square root of x
  5. Offline

    ReputationRep:
    ahh i get that now, thank you

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