Find f x ( 1 , 0 ) and f y ( 1 , 0 ) and interpret these numbers as slopes for the following equation. f ( x , y ) = 4 − x 2 − 4 y 2 f x ( 1 , 0 ) = ? f y ( 1 , 0 ) = ?

Question

Find       f    x    (  1  ,  0  ) and       f    y    (  1  ,  0  ) and interpret these numbers as slopes for the following equation.   f  (  x  ,  y  )  =      4    −          x      2        −    4          y      2            f    x    (  1  ,  0  )  =  ?        f    y    (  1  ,  0  )  =  ?

Estaboortzfv · Accepted Answer

F    x    (  x  ,  y  )  =      ∂          ∂      x        (  4  −      x    2    −  4      y    2        )          1              /            2          =      1    2    (  4  −      x    2    −  4      y    2        )                  1        2            −      1            ∂          ∂      x        (  4  −      x    2    −  4      y    2    )    =      1          2              4        −                  x          2                −        4                  y          2                      ×  [  0  −  2  x  −  0  ]        F    x    (  x  ,  y  )  =            −      x              4      −              x        2            −      4              y        2              At point (1,0)      F    x    (  1  ,  0  )  =            −      1              4      −              1        2            −      4      (      0      )              F    x    (  1  ,  0  )  =  −      1          3            F    y    (  x  ,  y  )  =      ∂          ∂      y        (  4  −      x    2    −  4      y    2        )                  1        2                =      1    2    (  4  −      x    2    −  4      y    2        )                  1        2            −      1            ∂          ∂      y        (  4  −      x    2    −  4      y    2    )    =      1          2              4        −                  x          2                −        4                  y          2                      [  0  −  0  −  8  y  ]        F          y        (  x  ,  y  )  =            −      4      y              4      −              x        2            −      4              y        2                At   (  1  ,  0  )        F    y    (  1  ,  0  )  =            −      4      (      0      )              4      −              1        2            −      0              F    y    (  1  ,  0  )  =  0

Find f_x(1, 0) and f_y(1, 0) and interpret these numbers as slopes for the following equation. f(x,y)=sqrt(4-x^2-4y^2)

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