Question

Locate the absolute extrema of the function on the closed interval.
g(x) =x^1/5 , [−1, 1]
minimum (x, y) = ( )
maximum (x, y)= ( )

Answer 1

first find the derivative of this function

Answer 2

1/5x^4/5

Answer 3

thats the derivitive

Answer 4

...

Answer 5

so you are saying that : g(x):x^1/5

Answer 6

is the derivative

Answer 7

cause from the notaion it looks like just a function

Answer 8

no i found the derivtive and it came out to be 1/5x^4/5

Answer 9

okay, that seems more like it

Answer 10

mhm/

Answer 11

now, this this derivative is never zero

Answer 12

thus, this function has no critical numbers, therefore it has no extrema

Answer 13

IT DOES I JUST ENTERED dne AND IT MARKED IT WRONG

Answer 14

IT DOES I JUST ENTERED dne AND IT MARKED IT WRONG

Answer 15

okay, then evluate it at -1 and 1

Answer 16

I dont know how to could you please help me with that

Answer 17

Since this derivative does not go to zero, it can only then have possible extrema on the endpoints of the closed interval. So we have evluate the orginal function at these endpoints

Answer 18

oki

Answer 19

When a function is on a closed interval, the endpoints become the points of extrema

Answer 20

and thats especially true in this case, considering that the derivative never equals zero, which usually gives us our crtical points

Answer 21

hmm

Answer 22

so, evluate the orgianl function at -1 and 1. The lowest value is you min. The highest value will be you max

Answer 23

did you get the right answer?