by the product rule ....
f ' (x) = x^(4/5) (2)(x-6) + (4/5)x^(-1/5) (x-6)^2
= (-1/5)x^(-1/5) (x-6) [10x + 4(x-6) ]
= (-2/5)x^(-1/5) (x-6) (7x-12)
= 0 for critical numbers (max,min)
-1/5x^(-1/5) = 0 ---> no solution
x-6 = 0 ---> x = 6
7x-12=0 ---> x = 12/7
take it from there
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x)=x^(4/5)(x − 6)^2
1 answer
1 answer