SOLUTION: Find the equation of the tangent to the curve y= e^x +x which is perpendicular to the line 4y+x=0

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the equation of the tangent to the curve y= e^x +x which is perpendicular to the line 4y+x=0      Log On


   

Question 876638: Find the equation of the tangent to the curve y= e^x +x which is perpendicular to the line 4y+x=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Perpendicular lines have slopes that are negative reciprocals.
4y%2Bx=0
4y=-x
y=-%281%2F4%29x
So then the slope of the perpendicular line is,
m%2A%28-1%2F4%29=-1
m=4
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THe value of the slope of the tangent line is the value of the derivative at a point.
y=e%5Ex%2Bx
dy%2Fdx=e%5Ex%2B1
So then,
e%5Ex%2B1=4
e%5Ex=3
x=ln%283%29
y=e%5E%28ln%283%29%29%2Bln%283%29=3%2Bln%283%29
So the equation of the line is,
y-%283%2Bln%283%29%29=4%28x-ln%283%29%29
y-%283%2Bln%283%29%29=4x-4%2Aln%283%29
y=4x%2B3-3ln%283%29
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