Find the critcal points and using the second derivative test determine if local max/min exists or if the test is inconclusive.
x^4/2-12x^2

Question

Find the critcal points and using the second derivative test determine if local max/min exists or if the test is inconclusive. 
x^4/2-12x^2

shamil98 · Answer

$$\huge \frac{ x^4 }{ 2 } - 12x^2$$
is this your problem?

anonymous · Answer

When i took both derivatives i got,$$f \prime = 2x^3-24$$
and $$f \prime \prime$$ = 6x^2-24\]

anonymous · Answer

^^yes

shamil98 · Answer

nvm, you made a typo lol

anonymous · Answer

I factored out the first derivative to get, $$2x(x^2-12)=0$$.
Then i plugged in my points , -4,-1,2,and 4 in the 2nd derivative to get, a local max at -4, -1 and local min at 2, and 4

anonymous · Answer

oh i forgot my critical points are $$x=0,\sqrt{12}$$

shamil98 · Answer

yeah, mb , i was looking at the second derivative for a sec, you're right with the critical points

anonymous · Answer

so i just want to make sure that when i'm solving these, I must always factor out the first derivative not the second one correct?

shamil98 · Answer

yeah, i made mistake looking at the second derivative,
the critical points are found by taking the first derivative and seeing which values of x make the derivative zero

anonymous · Answer

oh ok