Calculus challenge problem part C and beyond

[mpm166]

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?

 

[Zurtex]

Is it not just a matter or letting in your equation: [itex]\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'(x) = 0 is the minimum.[/itex]

 

[mpm166]

any other suggestions people?
I still seem to be having trouble

 

[Motifs]

What is your trouble ?