Question

find all extrema for the following function
y=x^5 -2x^3 +3 on the interval [-10..10]

Answer 1

@zepdrix @triciaal

Answer 2

find y'

Answer 3

5x^4 -6x^2

Answer 4

cool set y' to 0 and solve for x

Answer 5

these numbers will be call your critical numbers

Answer 6

5x^4 - 6x^2 = 0?

Answer 7

yes we need to solve that equation for x

Answer 8

x^2 (5x^2 -6)=0

Answer 9

Yeah, that looks right! Now solve for the 2 values of x

Answer 10

x^2 =0 and 5x^2 -6=0

Answer 11

Exactly! So what are the values of x?

Answer 12

x=0 a d x= square root of 6/5

Answer 13

That's right! :D

Answer 14

\[x^2=a \implies x=\pm \sqrt{a}\]

Answer 15

Now @freckles has gotta lead you through the rest xD lol

Answer 16

thanks for the guidance :)

Answer 17

you're very welcome :)

Answer 18

so draw a number line with the three critical numbers
and just check the intervals
I sometimes use the first derivative and sometimes I used the second derivative to see if my critical numbers are max,min, or neither

Answer 19

I think with the numbers given it might be easier to use the first derivative

Answer 20

if a graph switches from decreasing to increasing at a critical number then you have a local min
if a graph switches from increasing to decreasing at a critical number then you have a local max

Answer 21

okay in my class we do find the second derivative so do u think i should for this one?

Answer 22

yes, i am familiar with that

Answer 23

so wait? are you saying you want to use the second derivative test instead?

Answer 24

no, but do we need to find it to show the work?

Answer 25

not if you are not using the second derivative test

Answer 26

have you drawn the number line I mentioned above?