Question: Given surface: y 2 xz + 3z 2 = 2xy 2 + 8z + 4 , i. Find the equation of the tangent plane at

Given surface: y2xz + 3z2 = 2xy2 + 8z + 4 ,

i. Find the equation of the tangent plane at point (1, 2, -1).

ii. Find the derivative of the equation you found in (i.), in the direction (0.6, 0, 0.4) .

iii. Find the equation of the normal line at point (1, 2, -1).

iv. At what point does the normal line in (iii.) meet the plane x+3y+2z = 10?

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