Question

f(x) = 2 + x^(2/3) find the critical values, intervals where f(x) is increasing, intervals where f(x) is decreasing, list any max or min points

Answer 1

\[f(x) = 2+ x ^{2/3)}\]

Answer 2

Thank you for that!

Answer 3

know of any website that plots ?

Answer 4

www.wolframalpha.com

Answer 5

i have that but it doesnt show how to find the rest

Answer 6

sorry about asking website for plot

Answer 7

first find derivative
\[\frac{2}{3 x^{1/3}}\]

Answer 8

at x=0 this is undefined, so this is our criticle value
\[\frac{2}{3 x^{1/3}}\]

Answer 9

The whole thing is never zero, so no other criticle value

Answer 10

check left and right of x=0

Answer 11

how to do that in this denominator

Answer 12

how to do what?

Answer 13

check for x=0

Answer 14

Criticle point is where either derivative function is zero or undefined
let's check for function=0
\[\frac{2}{3 (x)^{1/3}}==0\]
function is never zero

but at x=0 function is undefined

Answer 15

you wrote check left and right of x = 0 where do i check this

Answer 16

i am just trying to figure that out

Answer 17

Hold on, I am trying to plot

Answer 18

This is your function(look at blue line, ignore the red line)
http://www.wolframalpha.com/input/?i=x^(2%2F3)%20%2B%202&t=crmtb01

Answer 19

how is the minimum 2 when the graph extends below 2? on my graphing calculator it comes out completely different

Answer 20

graph is above to 2 2 to above -inf to 2 2 to inf domain

Answer 21

I see, wolfram alpha is graphing it wrong, trust your graphing calculator

Answer 22

There should not be a graph left of 0

Answer 23

appreciate that

Answer 24

how so?

Answer 25

try just graphing x^(2/3)

Answer 26

wolfram alpha is seriously flawed
http://www.wolframalpha.com/input/?i=cube+root+of+-8
http://tinyurl.com/3rffdsw

Answer 27

it spills out good derivatives though

Answer 28

Criticle point is where either derivative function is zero or undefined let's check for function=0
23(x)1/3==0
function is never zero but at x=0 function is undefined

Answer 29

didnt understand the critical value part still

Answer 30

i know u are trying to find where the equation is undefined how do i write the answer

Answer 31

criticle value is 0 because that's where function is undefined

Answer 32

cool will start a new thread shortly with another graph

Answer 33

Function in red, Derivative in Blue