how do i find the critical numbers for cube root of X+2 . I took the derivative of this and got (1)/[3(x+2)^(-2/3)]. is the next step setting this expression equal to 0?

Question

anonymous · Answer

yes

anonymous · Answer

but Im having problem solving for 0 at this point.

anonymous · Answer

one sec

anonymous · Answer

and consider the x that will make the equation undefined as a critical number

anonymous · Answer

make the derivative i mean

anonymous · Answer

so I have to substitute a value for x that will make this expression ---> (1)/[3(x+2)^(-2/3)].  equal 0?

anonymous · Answer

your derivative should be 3x^2+12x+12

anonymous · Answer

if I substitute -2 for x, the entire denominator equals 0. so would -2 b my critical number?

anonymous · Answer

yes you cant find a number that can make your derivative equal to 0 so -2 is the only critical number

anonymous · Answer

ohh okay!!! thanks a lot! :)

anonymous · Answer

@pineda isnt the derivative wrong?

anonymous · Answer

I think its right. I double checked it on my calculator

anonymous · Answer

it looks fine for me its $$1/3\sqrt[3]{x+2^{2}}$$

anonymous · Answer

is the equation $$(x+2)^{3}$$

anonymous · Answer

pineda100 is right

anonymous · Answer

its $$\sqrt[3]{x+2}$$

anonymous · Answer

yeah

anonymous · Answer

oh oops read it wrong

anonymous · Answer

^_^

anonymous · Answer

original equation is $$\sqrt[3]{ }x+2$$. sorry i coudlnt get the square root sign to appear completely

anonymous · Answer

ya then pineda is correct. my bad.

anonymous · Answer

okay thanks a lot for your help pineda and everyone else who contritbuted! much appreciated! :)