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  1. Consider the function f(x) = x4/3 − 4x1/3. Homework Help ✎

    1. Algebraically determine where f is increasing.

    2. Algebraically determine whether f is concave up or concave down at x = −1.

    3. Determine the x-coordinates of all points of inflection.

Where is f '(x) positive?

Solve f ''(x) > 0 and f ''(x) < 0.

An inflection point occurs where f ''(x) undergoes a sign change.
Sometimes that happens where f ''(x) = 0 and sometimes where f ''(x) = DNE.