Find by hand the intervals where the function is increasing and decreasing. Use this information to sketch a graph. y = x^4 - 8x^2 + 1

Question

Find by hand the intervals where the function is increasing and decreasing.  Use this information to sketch a graph. y = x^4 - 8x^2 + 1

anonymous · Answer

@abb0t  can u help?

anonymous · Answer

take the derivative and check the signs of that derivative

anonymous · Answer

$$y = x^4 - 8x^2 + 1 $$
$$y'=4x^3-16x=4x(x^2-4)=x(x+2)(x-2)$$ is the first step

anonymous · Answer

okay

anonymous · Answer

this will be negative on $(-\infty, -2)$ and also on $(0,2)$ 
is that fairly clear?

amistre64 · Answer

lol,  find "by hand" .... what does that even mean?

anonymous · Answer

okay

amistre64 · Answer

if i have to sit here and start carving a function on a stone tablet .. im gonna get real upset :/

anonymous · Answer

good question
i was using my brain

anonymous · Answer

in the old days they wrote in the sand

anonymous · Answer

lol

anonymous · Answer

so function is decreasing on 
((-\infy, -2)\) and also on $(0,2)$ increasing elsewise

anonymous · Answer

okay

anonymous · Answer

make that 
decreasing on $(-\infty, -2)$

anonymous · Answer

Okay i see

amistre64 · Answer

satelitte is cheating, i think you have to do this by first principles, not those modern derivative rules ...

anonymous · Answer

ohh lol okay