Problems showing the constraint of master theorem case three holds
The following shows that the second statement is false.

Define $f$ as follows:
$$ f(n) = \begin{cases} 4n^3 &amp; n \text{ is a power of }4, \\ n^2 &amp; \text{otherwise}. \end{cases} $$
Let $n = 2^{2k+1}$. Then $f(n) = n^2$ while
$$ T(n) \geq 2T(n/2) \geq 2f(n/2) = n^3. $$