For each of the following pairs of functions $f$ and $g$, determine if the level curves of the functions cross at right angles, and find their gradients at the indicated point.

(a) $f(x,y) = 5x+5y$, $g(x,y) = 5x-5y$.
Do the level curves of $f$ and $g$ cross at right angles? ? yes no
$\nabla f(2, 4) =$
$\nabla g(2, 4) =$

(b) $f(x,y) = x^{4}-y$, $g(x,y) = 4y+\ln\!\left(\left|x\right|\right)$.
Do the level curves of $f$ and $g$ cross at right angles? ? yes no
$\nabla f(2, 4) =$
$\nabla g(2, 4) =$