Posted by AH on .
Find the critical numbers of the function. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.)
f(x)=x^(4/5)(x − 6)^2

Math 
Reiny,
by the product rule ....
f ' (x) = x^(4/5) (2)(x6) + (4/5)x^(1/5) (x6)^2
= (1/5)x^(1/5) (x6) [10x + 4(x6) ]
= (2/5)x^(1/5) (x6) (7x12)
= 0 for critical numbers (max,min)
1/5x^(1/5) = 0 > no solution
x6 = 0 > x = 6
7x12=0 > x = 12/7
take it from there