(ii) Find the (two) directions one could begin to move to continue to be level if one is standing on the surconfront at $(3,4,13)$.

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Could someone please offer me some pointers on just how to approach a question of this kind? Thanks in advance.

For component i)...

i) For the maximum price of readjust, attempt taking the gradient.

The gradient vector is $$.

The maximum rate of readjust will certainly happen in the direction of $ = $.

The maximum rate of readjust is then $sqrt 4^2 + (3/2)^2 = sqrt 73/2$

As for part ii)...

To uncover the (two) directions one might start to move to remain level if one is standing on the surconfront at $(3,4,13)$, we have to uncover the direction perpendicular to the gradient of $f$ at $(3, 4)$, and this would be $pm $.

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