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

- anonymous

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- anonymous

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....

- anonymous

yeah hehe. kay thanks (:

- anonymous

your welcome

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## More answers

- anonymous

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

- anonymous

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

- anonymous

doing synthetic division now...big numbers ):

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

can i post the graph of the equation?

- anonymous

did you graph it yet? the derivsative graph?

- anonymous

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

- anonymous

ok get its roots and plug it in the original equation

- anonymous

are you familiar with newtons method of approximation?

- anonymous

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

- anonymous

no whats that?

- anonymous

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

- anonymous

oh well what do you have to do?

- anonymous

this is the graph

##### 1 Attachment

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

did you see the graph?

- anonymous

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?

- anonymous

I read the wikipedia one

- anonymous

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

- anonymous

how do I get the actual coordinates?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

and that should get me my minimum/maximum?

- anonymous

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......

- anonymous

is this your college subject calculus?

- anonymous

im in high school pre calculus!

- anonymous

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

- anonymous

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

- anonymous

its the first one

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

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