Find an equation of the tangent line to the graph of the equation x+y-e

bobbie71G

bobbie71G

Answered question

2021-09-12

Find an equation of the tangent line to the graph of the equation
x+yexy=3 at the point (2,2).

Answer & Explanation

svartmaleJ

svartmaleJ

Skilled2021-09-13Added 92 answers

Step 1
We have
x+yexy=3
Now find the first derivative
D(x+yexy)=D(3)
1+yexy+exyy=0
y+yexy=exy1
y(1+exy)=exy1
y=exy1exy+1
Now put x=2, y=2
y=e221e22+1
y=02=0
m=y'=0
Step 2
The tangent line is of the form y=mx+c
put x=2,y=2, m=0
y=mx+c
2=(0)2+c
c=2
So the equation of the tangent line becomes.
y=mx+c
y=(0)x+2
y=2
Step 3
Answer:
y=2 is the equation of tangent line.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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