For function: g(x) = (x – 8)^2/3

(a) Find the critical numbers. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)
(b) Find the open intervals on which the function is increasing or decreasing. (If you need to use or –, enter INFINITY or –INFINITY, respectively. Enter NONE in any unused answer blanks.)
Increasing:(or[ and )or]
Decreasing:" and "

Question

For function: g(x) = (x – 8)^2/3

(a) Find the critical numbers. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)
(b) Find the open intervals on which the function is increasing or decreasing. (If you need to use  or –, enter INFINITY or –INFINITY, respectively. Enter NONE in any unused answer blanks.)
Increasing:(or[ and )or]
Decreasing:" and "

anonymous · Answer

find the equation of the normal to y=xsinx at x=pi/2

anonymous · Answer

can you show me process too.

anonymous · Answer

not enough for me

anonymous · Answer

how do you do

anonymous · Answer

oho!! sorry

ℐℵk℣ⱱøƴȡ◆ · Answer

wat?

solomonzelman · Answer

Yeah, seriously... WHAT ??!!

anonymous · Answer

This came directly from my homework in calculus.

solomonzelman · Answer

By critical points the mean the restriction(s) for the domain ?

solomonzelman · Answer

In this case, since the denominator is odd, and all you get is,  `∛ (x - 8) ²`  you wouldn't have any domain restrictions, because with an oddth root, in this case cube root, you will never come up with an imaginary/complex number. 
You don't have any denominator that has a variable either.

solomonzelman · Answer

And you can see that when `x→±∞, y→±∞`   (as opposed to `x→±∞, y→∓∞`)
Right ?

anonymous · Answer

attachment

anonymous · Answer

That looks the same x+-inf, y+-inf as opposed to x+- inf, y+- inf

solomonzelman · Answer

You don't have the correct graph. I am sorry to say this

solomonzelman · Answer

actually, hold on

anonymous · Answer

I put it in my graphing calc, it should be that one...

solomonzelman · Answer

well so far I can predict that it is either top left, or bottom right corner.

anonymous · Answer

but i also have no clue how to do the beginning portion of this problem.. all i know how to do is graph it in my calc..

solomonzelman · Answer

Do you know how to graph a line ones you are given y=mx+b ?

anonymous · Answer

no.. :(

solomonzelman · Answer

So, you can't graph (for example)  y=4x+3  ?

anonymous · Answer

oh, i just put that in my calc in the y= function , yeah i can do that

solomonzelman · Answer

Noo..... can you graph `y=4x+3` by hand ?

solomonzelman · Answer

y=4x+3  let's plug in some random numbers for x,

y=4(1)+3
y=4+3
y=7,                So we know that when x=1, y=7.   Thus we get the point `(1,7)`

Can you derive couple points like I did just now? (By plugging in ANY number for x) ?

anonymous · Answer

y=4(2)+3
y=8+3
y=11
so then x=2 y=11

anonymous · Answer

$$g(x) = (x – 8)^{2/3}$$  take the derivative and see where it is undefined
that will be at $x=8$

anonymous · Answer

that is all,you can pretty much do it with your eyeballs