Question

Find the extreme values of f(x)=x^4 - 4x^3 -x^2 +12x -2

Answer 1

set derivative equal to 0
\[4x^{3}-12x^{2}-2x+12 = 0\]

Answer 2

4x^3-12x^2-2x+12=0

Answer 3

http://www.wolframalpha.com/input/?i=plot+4x%5E%7B3%7D-12x%5E%7B2%7D-2x%2B12

Answer 4

What are the extreme values though?

Answer 5

looks like all the roots are irrational so have to solve using calculator or newtons method if you know calculus
http://www.wolframalpha.com/input/?i=+4x%5E3-12x%5E2-2x%2B12%3D0

Answer 6

I don't know calculus... do you know the extreme values?

Answer 7

use a calculator, the link gives the approximate zeros to the derivative equation

Answer 8

I dont know how to put it into a calculator though... could you?

Answer 9

haha well i meant a graphing calculator, but i already did, look at wolfram link

Answer 10

Those x answers are the extremes? I thought there was supposed to be x and y values

Answer 11

wow yes the local min/max points have x,y values but to get those you have to set derivative equal to 0 then solve for "x" . That will give you the "x" coordinates where slopes are 0 thus indicating either a local min or local max (extreme values)

Answer 12

Hold up haha I'm confused. Are those three x values my answers or do I need more?

Answer 13

already told you...wait what class is this? you said you dont know calculus but the 1st step to this problem was taking the derivative...lol

Answer 14

Pre-calc

Answer 15

So (-.94,0), (1.14,0), and (2.8,0) are my answers for extreme values?

Answer 16

hmm for your class all you are expected to do for this problem is use your graphing calculator, graph the function, then use the "calc" "max/min" graphing tool to determine those extreme values

Answer 17

"y" values are not 0 ..... the graph we did was the derivative (slope) graph so slope was 0 at those points

Answer 18

so what should I write as my complete answer

Answer 19

use your graphing calculator lol
dont you know how to figure out the "y" values, given the "x" values

Answer 20

When I graphed it I got different values

Answer 21

@dumbcow you can't help? I really need the answer to this

Answer 22

just use wolfram its a great online calculator

http://www.wolframalpha.com/input/?i=f%28x%29+%3Dx%5E4+-+4x%5E3+-x%5E2+%2B12x+-2%2C+local+min

http://www.wolframalpha.com/input/?i=f%28x%29+%3Dx%5E4+-+4x%5E3+-x%5E2+%2B12x+-2%2C+local+max

Answer 23

Oh ok I see the max and min values! But how do I put that in (x,y) form? I see where the min and max is at what x is, but how do I formulate my answer lol

Answer 24

it gives both x and y values

Answer 25

So max would be (1.14,6.14) and the mins would be (-.94, -10) and (2.8,-2.6)?

Answer 26

yeah

Answer 27

So that's what I would write as my extreme values? Exactly like that?