3D World
Calculus
Level
3
If z = ( y - x ) ^2 Find the targent plane at ( 1 , 2 , 1 )
z = 2( y - x ) - 1
z = 2( x -y ) + 2
z = 2( x - y ) + 1
z = 2( y - x ) -2
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1 solution
In the xy plane is a line ( y - x ) = 0 and on it there is a parabola. If you imagine an axis a, perpendicular to ( y - x ) = 0 , on the xy plane. You'll see z = a^2 . So, for z= 1 we have a = 1 . Differenciate z( a ) for a = 1 and find the targent line z = 2a - 1 . As z = ( y - x )^2 , and z = a^2 . We have a = ( y - x ) . Therefore, the targent plane is just z = 2( y - x )-1