Question

what are the local minimum an maximum pints of this equation -1.28x4 + -33.36x3 + -323.41x2 + -1384.63x + -2206.60 ?

Answer 1

hi are you there? if this is a y or f(x) then differentiate it then equaled it to zero and find its roots, that rot will be your max or min point..just plug it into your original equation....

Answer 2

yeah hehe. kay thanks (:

Answer 3

your welcome

Answer 4

the derivative would be like y'=-5.12x^3 -100.8x^2 -646.82X -1384.63,,....NOW FIND ITS ROOTS OR ZEROES

Answer 5

TO FIND THE ROOTS HERE I THNK ITS EASIER TO GRAPH IT...OR USE SYNTHETIC DIVISION

Answer 6

doing synthetic division now...big numbers ):

Answer 7

lets try graphing the y'=-5.12x^3 -100.8x^2 -646.82X -1384.63,,...

Answer 8

can you tell what the asymptotic behavior with this equation is?

Answer 9

ok this is quartic equation,, so you have ti look for the family of curves of all the quartic equations behaviour....its like a sine wave but not quite as good as sine wave it wil touch the grap at x, 4 times in the graph

Answer 10

it will have 4 roots, and it will touch the x axis four times

Answer 11

can i post the graph of the equation?

Answer 12

did you graph it yet? the derivsative graph?

Answer 13

well it is a parent function picture so i took a picture with the shape of a quartic function and plotted points on the graph

Answer 14

ok get its roots and plug it in the original equation

Answer 15

are you familiar with newtons method of approximation?

Answer 16

if you have a calculus book its in there also its in the web

Answer 17

no whats that?

Answer 18

newtons method of aprox is good in finding he rots of equations..

Answer 19

oh well what do you have to do?

Answer 20

this is the graph

Answer 21

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/approx/newton.html

Answer 22

http://en.wikipedia.org/wiki/Newton%27s_method

Answer 23

y'=-5.12x^3 -100.8x^2 -646.82X -1384.63,,....NOW FIND ITS ROOTS OR ZEROES ..to find its roots use newton method of approx.here you wil find 3 roots,then this 3 roots you will then plug them into your origimal equation to find you max y or min y

Answer 24

did you see the graph?

Answer 25

it didnot download in my laptop bec my c is full..here i can help u with newtons method,did you read the website i gave u?

Answer 26

I read the wikipedia one

Answer 27

newtons formula is x2=xi-[f(x1)/f'(x1)]

Answer 28

how do I get the actual coordinates?

Answer 29

here your f(x)=5.12x^3-100.8x^2-646.82x-1384.63 now use derivative to find f'(x)?

Answer 30

f'(x)=15.36x^2-201.6x-646.82 now you can use newtons method formula to find the roots of f(x)=5.12x^3-100.8x^2-646.82x-1384.63

Answer 31

newton formula is x2=x1-[f(x1)/f ' (x)] start with x1 like -8, -9, -7, hope you are using a good calculator with this calculation

Answer 32

using x2=x1- [(5.12x^2-100.8x^2-646.82x-1384.63)/(15.36x^2-201.6x-646.82)]
i got a root of x=25.13527 now you can plug it on you original equation

Answer 33

x2=x1- [(5.12x^3-100.8x^2-646.82x-1384.63)/(15.36x^2-201.6x-646.82)]
im sorry that was 5.12x^3

Answer 34

just plug the root x =25.13527 here, f(x)=-1.28x4 + -33.36x3 + -323.41x2 + -1384.63x + -2206.60

Answer 35

and that should get me my minimum/maximum?

Answer 36

f(25.13527)=-1.28x^4 + -33.36x^3 + -323.41x^2 + -1384.63x + -2206.60= -789369.6612 yes this is one of the minimum y..........you will have to find 3 more roots......

Answer 37

is this your college subject calculus?

Answer 38

im in high school pre calculus!

Answer 39

i think in this problem they want you to learn how to graph this function, and to learn how to get the roots of the first derivative.....then to find its max or min y you will have to use the root to find the min n the max

Answer 40

i wish i could look at the graph you want to show me, is it the graph of y=f(x)=-1.28x^4 + -33.36x^3 + -323.41x^2 + -1384.63x + -2206.60..or the graph of
y'=f '(x)=5.12x^3-100.8x^2-646.82x-1384.63 ..trace it at x=0, then you can find the y axis which is max or min

Answer 41

its the first one

Answer 42

yes only the first one bec x^4 is quartic therefore it must have 4 roots and 4 max or min y...correction on the first root i check it again on my calculator it is x=25.14043077

Answer 43

ook i have another question... how do i know which one is the positive/negative/complex roots?

Answer 44

so when you plug this x=25.14043077 to the orig eq f(25.043077)= -1282838.114

Answer 45

ypu notice that this is neg 1.million which is hard to graph,,therefore you will need to use the newton method formula..thats the conclusion here,,,you will be using the newton formula again and guess again for the roots

Answer 46

oh well thanks soo much for your help i really appreciate it!

Answer 47

hope you will follow the procedure again and again to find the other 3 roots....good luck ....is this in college subject? or ap calculus in high school?

Answer 48

umm i go to an option school, and we dont really have ap classes, but there is advanced math...thats what i take

Answer 49

oh ok....whews this is really for college problem hehehe thats really advance calculus

Answer 50

ook i have another question... how do i know which one is the positive/negative/complex roots? if you remember the quadratic formula
x= [-b+-sqrt(b^2-4ac)/2a]...the equation is y=ax^2+bx+c

Answer 51

positive complex root is like x=(2+sqrt-4)/2 = (2+2i)/2= 1+i did you noticed the plus or positive sign? that a positive complex root..for conjugate or neg complex root its x=1-i