Check that the point $\left(-4,4,4\right)$ lies on the surface $\cos\!\left(x+y\right) = e^{xz+16}$.

(a) View this surface as a level surface for a function $f(x,y,z)$. Find a vector normal to the surface at the point $\left(-4,4,4\right)$.



(b) Find an implicit equation for the tangent plane to the surface at $\left(-4,4,4\right)$.