# cubic help

• Aug 25th 2008, 04:29 PM
psychosocial for life
cubic 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 PM
Jhevon
Quote:

Originally Posted by psychosocial for life
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

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: $\frac d{dx} x^n = nx^{n - 1}$

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 $\frac d{dx}[c f(x)] = c \frac d{dx}f(x)$. here, your $f(x)$ is $x^n$

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

(why did you choose such big numbers? :p)
Dont know but regreting it now
• Aug 25th 2008, 05:05 PM
Jhevon
Quote:

Originally Posted by psychosocial for life
thanks for the help

Dont know but regreting it now

okie dokie.

• Aug 25th 2008, 06:30 PM
psychosocial 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 PM
Jhevon
Quote:

Originally Posted by psychosocial 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)

$\underbrace{(x - a)(x - b)}_{\text{do these two first}}(x - c) = [x^2 - (a + b)x + ab](x - c)$

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:

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

now group the like terms and simplify

$x^3 - (a + b + c)x^2 + (ab + ac + bc)x - abc$
• Aug 25th 2008, 07:07 PM
psychosocial 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 PM
Jhevon
Quote:

Originally Posted by psychosocial for life
thank you again i found out what i did wrong. i got x^3-6x^2-31x-120

it should be + 120
• Aug 25th 2008, 07:09 PM
psychosocial for life
sorry miss type i got +120