Question

I was looking at the examples for solving Critical Points and I understand them but the question that I'm working on is ------> f(x)= x^4-2x, find the critical points and determine whether they are Max/Min/Neither. Assistance please, I tried to factor them down and but I'm not sure if my answer is correct or if I even did it properly!? I would appreciate any help, thanks :) p.s I'm a newbie to this 'Open Study' :)

Answer 1

ok first of all we have a polynomial of degree 4 with positive leading coefficient, so before we start we know it must look something like this

Answer 2

taking the derivative we get
\[f'(x)=4x^3-2\] and we want the critical points.
this one only seems to have one because if you set
\[4x^3-2=0\] you get
\[4x^3=2\]
\[x^3=\frac{1}{2}\]
\[x=\sqrt[3]{\frac{1}{2}}\] as the only critical point

Answer 3

Should I differentiate the function? f(x)= x^4-2x

Answer 4

yes. that is the first step
you get
\[f'(x)=4x^3-2\]

Answer 5

and as you can see this only has one zero, so there is only one critical point.
it has to be a minimum for sure because we know what the choices are for a 4th degree polynomial. i will draw the possibilites

Answer 6

okay thanks so much I forgot to differentiate! Brilliant

Answer 7

something like these