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

PoentWeptgj 2022-07-23 Answered
I was looking to implicitly differentiate
22 x 6 + 4 x 33 y + y 7 = 17
and 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?
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Answers (2)

tun1t2j
Answered 2022-07-24 Author has 13 answers
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
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glyperezrl
Answered 2022-07-25 Author has 5 answers
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
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