Chapter 12.6, Problem 45E

Level curves Consider the paraboloid f(x, y) = 16 – x²/4 – y^,2/16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P and verify that the tangent line is orthogonal to the gradient at that point.

45     $f\left(x,y\right)=12;P\left(4,0\right)$