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Find the critical numbers of f(x)= 9x^(2/3) - 3x

 Mar 28, 2016

Best Answer 

 #1
avatar+23245 
+10

Critical values occur when the first derivative is zero and when the first derivative is undefined.

 

f(x)  =  9x2/3 - 3x     --->     f'(x)  =  6x-1/3 - 3

 

f'(x) is undefined when x = 0; so one critical value is 0.

 

f'(x) = 0     --->     6x-1/3 - 3  =  0     --->     6x-1/3  =  3     --->     x-1/3  = 1/2     --->     x1/3  =  2     --->   x  =  8

 

Thus, another critical value is 8.

 Mar 28, 2016
 #1
avatar+23245 
+10
Best Answer

Critical values occur when the first derivative is zero and when the first derivative is undefined.

 

f(x)  =  9x2/3 - 3x     --->     f'(x)  =  6x-1/3 - 3

 

f'(x) is undefined when x = 0; so one critical value is 0.

 

f'(x) = 0     --->     6x-1/3 - 3  =  0     --->     6x-1/3  =  3     --->     x-1/3  = 1/2     --->     x1/3  =  2     --->   x  =  8

 

Thus, another critical value is 8.

geno3141 Mar 28, 2016

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