SOLUTION: Find an equation of the tangent line to the graph of the function at the given point: 1+ ln 7xy = e^(7x-y), (1/7,1)

Algebra ->  Test -> SOLUTION: Find an equation of the tangent line to the graph of the function at the given point: 1+ ln 7xy = e^(7x-y), (1/7,1)      Log On


   

Question 1189604: Find an equation of the tangent line to the graph of the function at the given point:
1+ ln 7xy = e^(7x-y), (1/7,1)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the tangent line to the graph of the function at the given point:
1%2B+ln+%287xy%29+=+e%5E%287x-y%29, (1%2F7,1)

1%2B+ln+%287xy%29+-+e%5E%287x-y%29=0

log%28x%29+%2B+log%28y%29+%2B+log%287%29-+e%5E%287x+-+y%29=0

%28d%2Fdx%29%28log%28x%29+%2B+log%28y%29+%2B+log%287%29%29=1%2Fx

%28d%2Fdx%29%28e%5E%287+x+-+y%29%29=+7+e%5E%287+x+-+y%29

y'%28x%29=1%2Fx-7e%5E%287x+-+y%29


evaluate at (1%2F7,1)

+1%2F%281%2F7%29-7+e%5E%28%287%281%2F7%29%29+-+1%29=7-7e%5E%281-1%29+=7-7%2Ae%5E0=7-7%2A1=0

slope of tangent is m=0, so the line will be of the form y=a
given point (1%2F7,1), and tangent line is
y=1

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