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Find the positive value of x where fx=x3+2x1/3 has a horizontal tangent line.

Answer =

  • Calculus -

    I will assume you meant:
    f(x) = x^3 + 2x^(1/3)

    then f'(x) = 3x^2 + (2/3)x^(-2/3)
    for a horizontal tangent, f'(x) = 0
    3x^2 + (2/3)/(x^(2/3)) = 0
    multiply by x(2/3)
    3x^(8/3) = -2/3
    x^(8/3) = -2/9
    x = (-2/9)^(3/8) , which is undefined (can't take an even root of a negative)

    Unless you typed something different from what I assumed, there is no horizontal tangent.


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