Question

Help (Attached below) Determine the extrema of below on the given interval

Answer 1

i know we have to find the derivative and set it to zero

Answer 2

i got x= 8 and x= 2/9

Answer 3

now to have the intervals, im a little lost on...

Answer 4

would there only be 2 intervals?

Answer 5

or 3? 0-2/9 then 2/9-8 and 8-infinity?

Answer 6

ok... so whats the derivative...?

Answer 7

9x^2-74x+16

Answer 8

then i set it to = 0

Answer 9

ok... so what are the solutions...?

Answer 10

x=8 and x=2/9

Answer 11

critical numbers

Answer 12

yep... so on [0, 4] substitute x = 0, 2/9 and 4 into the original equation and find the corresponding values...

Answer 13

why 4?

Answer 14

thanks

Answer 15

isn't 4 a y?

Answer 16

and what 8?

Answer 17

because the 2 critical numbers are 8 and 2/9

Answer 18

well (a) is asking for the location of that min and max on the interval x = 0 to x = 4

and as x = 2/9 is a critical point...you don't know its nature

Answer 19

ooooooh, 8 would be the other one

Answer 20

let me try it

Answer 21

so the value x =0 is f(0) = 2

x = 2/9 f(2/9) = 3.76

x = 4 f(4) = ?

Answer 22

-334

Answer 23

so the max is 3.76 and min is -334?

Answer 24

thats correct...

Answer 25

so just test x = -9, x = 8 and x = 9... and see what happens... I think x = 2/9 remains the max

Answer 26

its an add interval since x = -9 gives a very large negative number