$$\bar{V}\phi = i\frac{\partial}{\partial x}(x^4 + y^4 + z^4) + j\frac{\partial}{\partial y}(x^4 + y^4 + z^4) + k\frac{\partial}{\partial z}(x^4 + y^4 + z^4)$$ $$\bar{V}\phi = i 4x^3 + j4y^3 + k4z^3$$

At (1, -2, 1) $\bar{V}\phi = 4i - 32j + 4k$

$$\overline{AB} = \bar{B} - \bar{A} = (2i + 6j - k) - (i - 2j + k) = i + 8j - 2k $$ Directional derivative at A in direction of $$\overline{AB} = (4i - 32j + 4k)\frac{i = 8j - 2k}{\sqrt{1^2 + 8^2 + 2^2}}$$ $$= \frac{4 - 32 * 8 - 8}{\sqrt{69}}$$ $$= \frac{-260}{\sqrt{69}}$$

Maximum directional derivative of $\phi$ at (1,-2,1)

$$\bar{V}\phi = 4i - 32j + 4k$$ $$|\bar{V}\phi| = \sqrt{4^2 + (-32)^2 + 4^2} = \sqrt{1056} = 4\sqrt{66}$$