Question

Find all relative extrema of the function. (If an answer does not exist, enter DNE.)
h(x) = 8(x − 9)^3

Answer 1

So to find F' wouldn't it be 21(x-9/0/62 and that makes the critical number x=9?? So what would relative extrema be?

Answer 2

Oops, it should be F' 21(x-9)^2

Answer 3

f'(x) = 8*3 (x-9) ^(3-1)

Answer 4

= 24(x-9)^2

Answer 5

Right, i got that part.. so what does relative maximum and relative minimum mean?

Answer 6

x= 9 is critical point
now you analyze f'(x) at f'(1) and f'(10). If it doesn't go from positive to negative or negative to positve, then you have no extrema
and the answer would be DNE.
analyza it though

Answer 7

I got 1536 for F'(1) and then F'(10) 24.. so since they are both positive then it should be DNE for minmum and maximum then?

Answer 8

???????

Answer 9

Yes :) DNE

Answer 10

ok, thank you :)

Answer 11

You're welcomed! :)

Answer 12

I'm double checking, there is no relative minimum of (9,0)?

Answer 13

No, trust me, there's none.
Just by looking at f"(x) you can tell that there's no max nor min,
usually anything (x+n)^2
or (x-n)^2 on the first derivative means there's no max or min on the original graph
just FYI so you won't have to calculate these later.

Answer 14

oh ok :) thanks for breaking it down!! :)