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what is the critical point for f(x)=x^(1/3)?

Guest Mar 30, 2017
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 #1
avatar+17693 
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A critical point occurs where the first derivative is either zero or does not exist.

First, find the first derivative:  f'(x)  =  (1/3)·x-2/3  

The first derivative will be undefined when x = 0.

geno3141  Mar 30, 2017
 #2
avatar+79654 
+1

f(x)  = x^(1/3)

 

f'(x)  = (1/3)x^(-2/3)    this derivative is undefined when x  = 0......so this is a critical point

 

See  the graph here :

 

https://www.desmos.com/calculator/w5bqt2akbh

 

As the graph shows......we have vertical tangent  at x  = 0

 

 

cool cool cool

CPhill  Mar 30, 2017

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