Problem

Let $ f(x) = cx + \ln(\cos x). $ For what value o…

00:54

Problem 36 Hard Difficulty

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.

Name: find equations of the tangent lines to the curve y ln xx at the points 1 0 and e 1e illustrate by gr
Uploaded: 2019-12-05
Duration: 2 min 15 s
Channel: Numerade
Description: 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.

Answer

$y=x-1$ and $y=\frac{1}{e}$ and graph

Grace H.

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College

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Video Transcript

if this problem were given a function. Why, as natural look affects the line by ex that were given teeth points and where are the questions off tension lines that passes through the first given set of points and second set of points. Now we know that the question of potential in you for a while in this point of physical, through derivative you want that given point times explains Excellent. So you personally to find a wayto dysfunction Why Prime of X, uh, revenge this school circle. So it'll be there. We talked to function in a new writer months by ancient denominator minus functioning numerator most by five records Continent, you know, nature divided by function in your spirit. So we can write this one as then 11 Distinction. Look off extra by experience. A less away the derivative at given for inside. So when exports and one exit e when it says one, we find everything to be one on one Instruction will afford one. That is, since that you look upon it. Zero Eredivisie one also excited to eat. We find every two as 11 is natural logo He divided by each for natural ago. Physical 11 minus one is zero. So their return order slope at this 00.0 All right, since we know very motives now let's find the questions off dependent lines. We have one witness. Zero is equal to one times experts for promised The first things that line is why is it would explain. And the 2nd 1? We have one minus one over. Eat the soup of the zero times exports E. So from this, we see that the question of things like this. Then why is he so? It will be just and horizontal line. All right. Here. This given red skirt is orginal function. Why this green present? A line is Why's it e? And this blue line is a straight line, and that is the first tension line is you can see its first things like this. Um, engine director at this given 0.10 Also, this is what X is equal to B y Z before

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