Calculus
posted by Suzy .
26. Find all points of inflection.
f(x) = (5x3)^(1/3)
Note: I have gotten
f''(x) = (50/9)(5x3)^(5/3)
I would like to know how to figure out the zeros.

you want to have (50/9)(5x3)^(5/3) = 0
then (5x3)^(5/3) = 0
or
1/(5x3)^(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.