SOLUTION: Find the value of x for which the tangent line to {{{y=2x^2 + 1}}} will be parallel to the tangent line to {{{y = 4ln(x) - 3}}}?

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Question 1153632: Find the value of x for which the tangent line to y=2x%5E2+%2B+1 will be parallel to the tangent line to y+=+4ln%28x%29+-+3?
Found 3 solutions by MathLover1, Alan3354, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find the value of x for which the tangent line to y=2x^2+1 will be parallel to the tangent line to y=4ln(x)-3?
first find differentiate:
y+=+2x%5E2%2B1
dy%2Fdx+=+4x
y+=+4ln%28x%29%2B3
dy%2Fdx+=+4%2Fx
parallel lines have equal slopes
the slopes are equal when:
4x+=+4%2Fx
x%5E2=1
x+=+1 or x+=+-1
The second function is undefined at x=-1; so x=1 is what we are looking for.
For the first function,
f%281%29+=+2%281%5E2%29%2B1+=+2%2B1+=+3
For the second function,
f%281%29+=+4ln%281%29%2B3+=+4%280%29%2B3+=+3
The slopes of the two graphs are the same at (1,3); and the two graphs are tangent to each other at that point.
At+x=1, the slope of both graphs is 4; the line with slope m=4 passing through (1,3) is y+=+4x-1
A graph, showing the two curves and the common tangent line:
graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C2x%5E2%2B1%2C4ln%28x%29%2B3%2C4x-1%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of x for which the tangent line to y=2x%5E2+%2B+1 will be parallel to the tangent line to y+=+4ln%28x%29+-+3?
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Slope of y=2x%5E2+%2B+1 = 4x.
Slope of y+=+4ln%28x%29+-+3 = 4/x
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4x = 4/x
x = 1
==================
The 2 slopes are 4 so they're parallel.
There are an infinite # of other slopes tangent to the 2 curves that are parallel.
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Mathlover switched to y+=+4ln%28x%29+%2B+3
Maybe that's what you meant?
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I'm not blind, but I do use reading glasses.
IDK how I was supposed to spot the alleged plagiarism, but I'm not overly worried about that.
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What I find interesting is that only x = 1 is a solution algebraically, but there are an infinite # of other lines that are parallel to the 2 graphs.

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of x for which the tangent line to y=2x%5E2+%2B+1 will be parallel to the tangent line to y+=+4ln%28x%29+-+3?
Is @Alan3354 blind? Can't he see that @ MATHLOVER has plagiarized someone else's work (see Miscellaneous_Word_Problems/1153638/Answers 775890 and 775891).

I wish I had the authority to jail people who STEAL other people's work and present it as their own. I would give them MAXIMUM IMPRISONMENT

and ISOLATE them from others. 



A word to the person who CLAIMS to love math: 

What do you gain by PLAGIARIZING someone's work? If you want to use someone's else's work, DON'T present it as your own. Let the reader know that

you're using someone else's work by CITING the AUTHOR of the work you're copying and presenting. Did you even notice that when you PLAGIARIZED 

this particular person's work, you also presented his ERROR also. 

You need to STOP!! This is not the 1st time I've seen you do it! STOP!!!



I understand, @ALAN. Ha, ha, ha, ha!