Question

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.

Answer 1

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