we were given a function of y=(x-a)(x-b)(x-c) and were told to add in our own numbers i chose y=(x-8)(x+5)(x-3). can some one show me the working to get it to a cubic and then the derivative

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- Aug 25th 2008, 04:29 PMpsychosocial for lifecubic help
we were given a function of y=(x-a)(x-b)(x-c) and were told to add in our own numbers i chose y=(x-8)(x+5)(x-3). can some one show me the working to get it to a cubic and then the derivative

- Aug 25th 2008, 04:37 PMJhevon
lets say it was (x - 8)(x + 5), could you expand that?

expand the first two first, and then multiply what you got by the (x - 3). how? first multiply everything by the x and then multiply everything by the -3

when finding the derivative, all that is needed is the power rule: $\displaystyle \frac d{dx} x^n = nx^{n - 1}$

and of course, if there are constants in front of the x's, you just leave them and multiply what you got by them since $\displaystyle \frac d{dx}[c f(x)] = c \frac d{dx}f(x)$. here, your $\displaystyle f(x)$ is $\displaystyle x^n$

(why did you choose such big numbers? :p) - Aug 25th 2008, 05:04 PMpsychosocial for life
thanks for the help

Quote:

(why did you choose such big numbers? :p)

- Aug 25th 2008, 05:05 PMJhevon
- Aug 25th 2008, 06:30 PMpsychosocial for life
for some reason it still isnt working out right could you please show me the working out so i can workout what im doing wrong. i just cant work it out (Crying)

- Aug 25th 2008, 06:58 PMJhevon
$\displaystyle \underbrace{(x - a)(x - b)}_{\text{do these two first}}(x - c) = [x^2 - (a + b)x + ab](x - c)$

now we take the x in the second set of brackets and multiply everything in the first set, after that, we take the -c in the second set of brackets and multiply everything in the first set. so we get:

$\displaystyle \underbrace{x^3 - (a + b)x^2 + abx}_{\text{everything in the first set times }x}~~~ \underbrace{- cx^2 + c(a + b)x - abc}_{\text{everything in the first set times }-c} $

now group the like terms and simplify

$\displaystyle x^3 - (a + b + c)x^2 + (ab + ac + bc)x - abc$ - Aug 25th 2008, 07:07 PMpsychosocial for life
thank you again i found out what i did wrong. i got x^3-6x^2-31x-120

- Aug 25th 2008, 07:07 PMJhevon
- Aug 25th 2008, 07:09 PMpsychosocial for life
sorry miss type i got +120