What is the equation of the normal line of #f(x)=e^x/x# at #x=1 #?
First, find the point the normal line will intercept.
The normal line will pass through the point
Now, to find the slope of the normal line, we must first find the slope of the tangent line. Thinking ahead, once we find the slope of the tangent line at
First, find the derivative of the function, will require the quotient rule.
The slope of the tangent line is
This is a rather odd case. This is a horizontal line, since it has a slope of
The vertical line that passes through the point
Graphed are the function and its normal line: