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posted by  lotus_daemon on 11/18/2008 11:32:44 PM  |  status: Live  

Tangent lines to curve

Course Textbook Chapter Problem
Calculus Calculus (4th) by Stewart 3.7 24
Question Details:
Find equations of the tangent lines to the curve y = ln(x)/x at the points (1,0) and (e,1/e). Illustrate by graphing the curve and its tangent lines.

My friend and I weren't sure whether or not to start with the quotient rule and got stuck. Help would be greatly appreciated. Thank you in advance.

*always needs help in Calculus*

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Oracle
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posted by Grace on 11/19/2008 12:00:02 AM  |  status: Live
Asker's Rating: Lifesaver   
lotus_daemon's comment:
"It seems that we did the 1st part right. Thank you for clarifying this and helping us on the 2nd part. e^x was pretty intimidating."
Response Details:
You need two things to make the equation of a line: slope and a point. The given info indicates that there are two separate parts to the problem.
Recall slope = derivative.
y ' =

a) equation of tangent line at (1,0)
Evaluate slope/derivative at given point: f ' (1) =
point-slope form: y-y1 = m(x-x1)
y - 0 = (1)(x - 1)
y = x-1

b) equation of tangent line at (e , 1/e)
Evaluate slope/derivative at given point: f ' (e) =
point-slope form: y-y1 = m(x-x1)
y - 1/e = (0)(x - e)
y -1/e = 0
y = 1/e


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