Second Derivative of a Curve: Solving for x | Finding d2y/dx2=0

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Homework Help Overview

The problem involves finding the value of x for which the second derivative of the curve defined by the equation y=e^(2x)-x^2+x-3 equals zero. The subject area pertains to calculus, specifically the analysis of derivatives.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the process of finding the first and second derivatives of the given function. There are questions about the steps taken to derive certain equations, particularly the transition from one form of the equation to another. Some participants express confusion regarding the reasoning behind specific equalities and the implications of the derivatives.

Discussion Status

The discussion is ongoing, with participants providing hints and questioning each other's reasoning. There is a recognition of the need to clarify steps in the derivation process. Some participants have offered guidance while others emphasize the forum's policy against providing complete solutions.

Contextual Notes

Participants are reminded of the forum's policy to avoid presenting full solutions, focusing instead on hints and guidance to foster independent problem-solving.

ibysaiyan
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Homework Statement


A curve has equation y=e^2x-x^2+x-3 , find value of x for which d^2y/dx^2=0.


Homework Equations





The Attempt at a Solution


well. i started by finding out the 1st and 2nd derivative:
y=e^2x-x^2+x-3
dy/dx= 2e2^x-2x+1 and d2y/dx2=4e^2x-2 = 0

dy/dx =>2e^2x=2x-1
=>e^2x = 2x/2 -1/2
e2x= x-1/2 (1)

sub. value (1) into: d2y/dx2.
4e^2x-2= 0
e^2x = 1/2
e^2x = 1/2 (x-1/2)
no idea.. on what to do now =/.
Thanks in adv.
 
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ibysaiyan said:
dy/dx =>2e^2x=2x-1
=>e^2x = 2x/2 -1/2
e2x= x-1/2 (1)

I don't know what you did here (why is 2e^2x=2x-1? dy/dx doesn't have to equal 0), but you already got 4e^2x-2 = 0 in the previous step. Just solve for x and you're done.
 
How did you go from e^(2x)=1/2, which looks ok, to e^(2x)=(1/2)*(x-1/2) which does not look ok? If it's after 4AM there, I suggest you take a nap.
 
Oh k, yea. i can barely hold my eyes lol, alright i guess i will sleep now, thanks for the replies and helping me out :), i will be back tomorrow.Good night for now.
 
...
try to use the inverse operation of the exponential
 
Last edited:
The policy of the forum is not to present solutions for problems, ok? Just give hints. Never do that again, ok? I'm not going to hit the Report button. But I will next time. ibysaiyan could have gotten this on his own. Don't you see the value in that?
 
Last edited:
:[ sorry sorry, i won't do it again
...is it better now ? :D
 
nesteel said:
:[ sorry sorry, i won't do it again
...is it better now ? :D

Much better, thanks!
 

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