Consider the R2 −R function f defined by f (x,y) = xy and let C be the contour curve of f at level 4.
(a) Find a Cartesian equation for the tangent L to C at (x,y) = (1,4).
(b) Sketch the contour curve C together with the line L in R2.
(c) Find an equation for the tangent plane V to the graph of f at (x,y) = (1,4).
(a) Here, slope of tangent at x=1 is:
Equation of tangent line L to C at (1,4) is
(b)
(c) Here,
Equation of tangent plane at (1,4) is
Hence, is equation of tangent plane V at (1,4)
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