Consider the following hx Find the critical numbers Enter y

Consider the following.

h(x) =

Find the critical numbers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

x =

Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

X^3

x 9

Solution

I understand the function h(x) = x3 ( sqrt( x-9) )

To find critical numbers: h\'(x) = 3x^2 (sqrt(x-9) + x^3/sqrt( x-9)

h\'(x) =0

3x^2 (sqrt(x-9) + x^3/sqrt( x-9) =0

3x^2(x-9) +x^3/2sqrt(x -9) =0

x^2 (7x -54) =0

x =0 , x = 54/7

As in f(x) domain is x >=9

So, at x=0, x= 54/7 its a complex value of f(x)

So, there are no critical points