1) Find the critical numbers of the functionf(x) =x^2/3(8x)

and then determine if each critical number defines a local maximum or local minimum of the function or neither. (If an answer does not exist, enter DNE.)

-smaller value x=

Which of the following would the answer be: local maximum, local minimum, neither, or no critical points ?

-larger value x =

Which of the following would the answer be: local maximum, local minimum, neither, or no critical points ?

and

2) Find the critical numbers, if any, of the functionf(x) = 3x⁵50x³+135x+5

and then determine if each critical number defines a local maximum or local minimum of the function or neither. (If an answer does not exist, enter DNE.)

smallest value x =_________ Which of the following would the answer be: local maximum, local minimum, neither, or no critical points ?

smallest value #2 x=________Which of the following would the answer be: local maximum, local minimum, neither, or no critical points ?

smallest value #3 x=_______ Which of the following would the answer be: local maximum, local minimum, neither, or no critical points ?

largest value x=____________ Which of the following would the answer be: local maximum, local minimum, neither, or no critical points ?

and

3) Find the global minimum and maximum of the continuous functionf(x) =x²8 ln(x) on[1,4].

(Round your answers to two decimal places.)

find global minimum value____________ and global maximum value_______________