## Question

###### Find an equation of the tangent plane and parametric equations of the normal line to the surface at the given point z=-9+4x-6y-x^2-y^2 (2,-3,4) Find the relative extrema. A) f(x, y) = x3-3xyザ B)...

find an equation of the tangent plane and parametric equations of the normal line to the surface at the given point z=-9+4x-6y-x^2-y^2 (2,-3,4)

Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-

## Answers

Given surface is z =-9 +4x-oy-ґ-y Suppose/ (x,y.z)-' +y' -4x+6y+z+9 -2x- 4 Of Of P2.-34) Pr2.-3.4) The equation of the tangent plane at P(a,b,c)is Oy (i)Therefore the equation of the tangent plane at P(2,-3,4)is ()The equation of the normal i line at P(a,b,c)is x-a 2-C Of Therefore the equation of the normal line at P (2,-3,4)is

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