Consider the function $f(x) = x^{4/3} − 4x^{1/3}$.

1. Algebraically determine where $f$ is increasing.

   Hint (a):

   Where is $f^\prime(x)$ positive?

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

   Hint (b):

   Solve $f^{\prime\prime}(x) > 0$ and $f^{\prime\prime}(x) < 0$.

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

   Hint (c):

   An inflection point occurs where $f^{\prime\prime}(x)$ undergoes a sign change.
   Sometimes that happens where $f^{\prime\prime}(x) = 0$ and sometimes where $f^{\prime\prime}(x) =$ DNE.