Question

1) Find all the critical numbers of the given function

f(x) = X 1 - 4
-
3

Answer 1

(0,-4)

Explanation:

Given

`f(x) = x^(1)/(3) - 4`

Required

Determine the critical numbers

`f(x) = x^(1)/(3) - 4`

Differentiate:

`f'(x) = (1)/(3)x^{(1)/(3) - 1}`

`f'(x) = (1)/(3)x^{-(2)/(3)}`

Equate to 0

`f'(x) = (1)/(3)x^{-(2)/(3)} = 0`

`(1)/(3)x^{-(2)/(3)} = 0`

Multiply through by 3

`3 * (1)/(3)x^{-(2)/(3)} = 0*3`

`x^{-(2)/(3)} = 0`

`x = 0`

Substitute 0 for x in
`f(x) = x^(1)/(3) - 4`

`f(0) = 0^(1)/(3) - 4`

`f(0) = 0- 4`

`f(0) = - 4`

Hence, the critical point is: (0,-4)