Answer:Directional derivative = $\bigtriangledown \phi=\frac {\partial \phi}{\partial x}+\frac {\partial \phi}{\partial y}+\frac {\partial \phi}{\partial z}$

$\phi =x^2y^2z^4\\ \frac {\partial \phi}{\partial x}=2xy^2z^4\\ \frac {\partial \phi}{\partial y}=2x^2yz^4\\ \frac {\partial \phi}{\partial z}=4x^2y^2z^3\\ \bigtriangledown \phi=\frac {\partial \phi}{\partial x}+\frac {\partial \phi}{\partial y}+\frac {\partial \phi}{\partial z}=2xy^2z^4i+2x^2yz^4j+4x^2y^2z^3k\\ (\bigtriangledown \phi) _(3,-1,2)=2(3)(-1)^2(2)^4i+2(3)^2(-1)(2)^4j+4(3)^2(-1)^2(2)^3k\\ (\bigtriangledown \phi) _(3,-1,2)=96i-288j+288k\\ $

Directional derivative at (3,-1,2)= 96i -288j+288k

Directional derivative of $\phi$  is maximum in the direction of $\bigtriangledown \phi$ i.e . in the direction of 96i-288j+288k

The maxmium magnitude =$|\bigtriangledown \phi |=\sqrt {(96)^2+(-288)^2+(288)^2} \ |\bigtriangledown \phi |=418.4542 \$