I was looking to implicitly differentiate − 22 x 6 + 4 x 33 y + y 7 = − 17and found it to be d y d x = 132 x 5 − 132 x 32 y 4 x 33 + 7 y 6 Now, I am trying to find the equation of the tangent line to the curve at the coordinate (1,1). So I then plug both 1 in for x and y into the above equation and come up with 0 11 Now I go to solve y − y 1 = m ( x − x 1 )getting y − 1 = 0 ( x − 1 )resulting in y = 1 and the equation to be y = x + 1 for my final answer. Am I going about this in the correct manner?

Question

I was looking to implicitly differentiate  −  22      x    6    +  4      x          33        y  +      y    7    =  −  17and found it to be                    d        y                    d        x              =                    132                  x          5                −        132                  x                      32                          y                    4                  x                      33                          +        7                  y          6                    Now, I am trying to find the equation of the tangent line to the curve at the coordinate (1,1). So I then plug both 1 in for x and y into the above equation and come up with            0      11      Now I go to solve  y  −  y  1  =  m  (  x  −  x  1  )getting  y  −  1  =  0  (  x  −  1  )resulting in   y  =  1 and the equation to be   y  =  x  +  1 for my final answer. Am I going about this in the correct manner?

tun1t2j · Accepted Answer

Your work is fine but since   m  =            (                        d          y                          d          x                    )              (      1      ,      1      )        =  0 we have  y  −      y    1    =  m  (  x  −      x    1    )  =  0    ⟹    y  =  1

glyperezrl · Accepted Answer

your calculations for the slope of tangent are correct. The only point that you have missed is the last step of finding the equation of tangent line which is simply   y  =  1 not   y  =  x  +  1

I was looking to implicitly differentiate −22x^6+4x^(33)y+y^7=−17

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