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and how's it going until now?

For example On (a) do I have to find roots for only f(x) or f'(x) and f''(x) ?

it says find roots of f

ooh first = 3/2

second,third = (-6 +- sqrt(72))/2

Which brings me to another problem of mine on how to actually point this number on the graph

(it's (-6 ± sqrt(0)) / 2 )

ah yea that's true

so we have one root for 3/2 and one for -3

for b I just find f(0) of the function ?

yes

-27

yes again ;)

So the intervals (-inf,-9) increase
(-8,0) decrease
(0,inf) increase
At least thats what I got

the derivative of the function is \(6x(x+3)\). the intervals are (-inf,-3), (-3,0), (0,inf)

arent we using multiplication rule for the derivative

or was it a typo?

it wasnt a typo but I guess you are right on that one

oops. last one is
\[ 2(x+3)\times [(x+3) + (2x-3)] = 2(x+3)[3x] = 6x(x+3)\]

hm let me redo it

2(x+3)^2 +4x^2 + 12x - 4x -12 up until now all correct?

i don't think so.
do you apply the rule on \((2x-3)(x^2+6x+9)\) ? what's your starting point?

Yes I apply the rule however i start with the product rule first before applying it

show the first steps plz

2(x+3)^2+2(x+3(2x-3)

2(x^2+6x+9)+2(x+3)(2x-3)

those are correct?

Why mistake what do you multiply first with what

ok ok I got it now for concave up/down (-inf,-1) down (-1,inf) up

infection points x=-1

and I am stuck at (f)

Yea I see now are my next moves correctly done??

you mean for f''(x) I got it wrong?

I damn you are right

\(f'\) is unfortunately wrong, so you could not get the right \(f''\).

(-inf, -3/2) down (-3/2, inf) up I get it now

right?

\(f''(x) = (6(x^2+3x))' = 6(2x+3)\) with root x=-3/2. -> inflexion point at -3/2.

Bro I mean concave up down :D I moved a step

I understood the previews one

I am just stuck at (f) could you help me out surpass it?

only for f'(x) and f''(x) ?

is not a min nor a max at -3 0

so I dont use -3/2 at all? I can only just use the roots of the first derivative for the second?

first step: a few points
|dw:1369666161790:dw|

then join using use \(f''\) at the extrema (-3 and 0)
|dw:1369666278751:dw|

join in a healthy way (without forgetting hte inflexion point)
|dw:1369666362664:dw|