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nickersia Group TitleBest ResponseYou've already chosen the best response.0
Part d, help anyone? Thanks :)
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
Would you please start the necessary work, and share with us what you have done. also, please explain what it is that you need to know. Let's build upon what you do already know.
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
Everything is on the picture, I've done parts a,b and c, and I don't know how to do part d
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
Your work is very neat. I apologize for not having scrolled down to see what you'd already done. Let me look at Part D. What do you think you need to know to answer Part D correctly?
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
\[yy _{1}=m(xx _{1})\] \[y (\frac{ 2 }{ 4 }1+\ln \frac{ 2 }{ 4 }) = \frac{ x _{a} 2}{ x _{a} ^{2} }(x4)\] where Xa is 4 because point B is (4,0.193)
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
y1 (this thing in the bracket) is equal to 0.193 which I got as a coordinate for B, and the slope of the tangent should be equal to derivative of y at point B
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
I'm going to assume that your point of inflection, (4,0.193), is correct. then \[x _{0}=4,y _{0}=0.193\] and you need only substitute these into the pointslope formula for the equation of a straight line. What is your assumed value for the slope, m?
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
\[m = \frac{ x2 }{ x ^{2} }\] where x is 4, so it gives me 0.125
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
Because \[\frac{ dy }{ dx } = m\]
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
Using your formula for the slope, and calculating the slope that way, I get the same result calculating the slope differently. I, too, get m=0.125, which is the same as 1/8. I'd suggest you substitute these numerical results into the point slope form. Point of tangency is (4,0.193), as before, and slope is either 1/8 or 0.125.
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
\[y0.193 = (?)*(x  ?)\]
 8 months ago

nincompoop Group TitleBest ResponseYou've already chosen the best response.0
the second derivative must equal zero to be an inflection point
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
@nincompoop, are you saying that the inflection point is not (4,0.193)?
 8 months ago

nincompoop Group TitleBest ResponseYou've already chosen the best response.0
I didn't look at his solution, but that is what to bear in mind when looking for the inflection point.
 8 months ago

nincompoop Group TitleBest ResponseYou've already chosen the best response.0
http://www.math.sc.edu/~diestelr/4.2Notes.pdf
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
I got it!
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
@nincompoop: If you haven't looked at Nick's solution, then commenting as you have is irrelevant and distracting. If you had found a mistake, then I would have wanted to hear from you.
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
\[y  (\frac{ 1 }{2 }+\ln2) = \frac{ 1 }{ 8 }(x4)\] . . . \[x8y+8(\ln21)=0\] The problem was that I didn't changed the slope with 1/8 at the beginning so it got more and unnecessary complicated.
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
@nickersia: Congrats! Again, I admire the neatness and precision of your work.
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
@nincompoop yes, I used that in part b) Thank you @mathmale ! :)
 8 months ago

mathmale Group TitleBest ResponseYou've already chosen the best response.1
Thanks for the medal and for becoming a fan of mine! Hope to work with you again soon.
 8 months ago

nickersia Group TitleBest ResponseYou've already chosen the best response.0
You're welcome, me too! Good luck :)
 8 months ago
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