Solving Calculus Challenge Problem - Part A & B Answered

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The discussion revolves around solving a calculus challenge problem, specifically parts a and b, with uncertainty about approaching part c. The user suggests using the equation ε = ε + Δε and differentiating the function V(x) = x^4 - 4x^3 + (ε + Δε)x^2 + δx + 5 with respect to x. They express confusion about the requirements of the question and the need to determine which V'(x) = 0 corresponds to a minimum. Other users are encouraged to provide additional suggestions to clarify the approach. The conversation highlights the complexities of calculus problem-solving and the need for collaborative input.
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I have this calculus challenge problem (found here: http://firstyr.appsci.queensu.ca/apsc171/chall1.pdf )

I was able to answer part a and b, however I am unsure how to approach c and onwards

does anyone have any suggestions?
 
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Is it not just a matter or letting in your equation: \varepsilon = \varepsilon + \Delta \varepsilon[/tex]<br /> <br /> So you have:<br /> <br /> V(x) = x^4 - 4x^3 + (\varepsilon + \Delta \varepsilon)x^2 + \delta x + 5<br /> <br /> Differentiating the above with respect to x, knowing that \delta x = 0 then equalising to 0 and solving for x and rearranging for \Delta \varepsilon? Not entirely sure what the question is asking so not sure.<br /> <br /> Although thinking about it you would probably have to show which V&#039;(x) = 0 is the minimum.
 
any other suggestions people?
I still seem to be having trouble
 
What is your trouble ?
 
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