26. Find all points of inflection.

f(x) = (5x-3)^(1/3)

Note: I have gotten
f''(x) = (-50/9)(5x-3)^(-5/3)
I would like to know how to figure out the zeros.

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  1. you want to have (-50/9)(5x-3)^(-5/3) = 0
    then (5x-3)^(-5/3) = 0
    1/(5x-3)^(5/3) = 0

    Clearly this has no solution.
    Think of it this way:
    1 divided by what number would give you zero?? There is no such number

    So since your equation has no solution, there is no point of inflection.

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