Second derivative

[jade adder]

Plz help me

[fringe oracle]

Just differentiate twice and make that expression equal 55, rearrange for x and your good!

[sullen breach]

differentiate and differentiate again
u will have an equation when you equal to 55

dy/dx = 1/3 x^3 + 6x

d^2/dx^2 = x^2 + 6

x^2 + 6 = 55

x^2 = 49

x = 7

(as they wanted the positive value)

[jade adder]

for dy/dx i got -1/3 x^5 + 6x

[willow granite]

ur power should be negative

for the first term

[jade adder]

yea i meant to type that

bcs i took the x out the fraction

then d^2y/dx^2 i got 5/3 x^-6 + 6

[sullen breach]

am i seeing this right?

that is y = 1/12 x^ 4 + 3x^2 + 4 right

[willow granite]

wdym

[jade adder]

y = 1/12x^4 + 3x^2 + 4

[sullen breach]

yes

so dy/dx should be 1/3 x^3 + 6x

[willow granite]

i always sort out the powers before doing any diffing

[jade adder]

make y = 1/12 x^-4 + 3x^2 + 4

i do that always

[willow granite]

,w diff x^-4/12 + 3x^2 + 4

,w diff again

[pseudo folio]

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[willow granite]

omds'

[jade adder]

thats trash

[sullen breach]

x should be 7

[willow granite]

7 is a nice number

so sounds about right

[jade adder]

i dont think thats right tho

[jade adder]

howd you get this

[sullen breach]

power rule multiply 4 by the fraction to get 4/12 = 1/3, then rreduce the power by 1

so x^4 -> x^3

1/3 x ^3

[jade adder]

i got -1/3 x^-5

im so lost

[sullen breach]

where are u getting negative from

its not x^-4

its x^4

perhaps u r reading the question wrong?

[jade adder]

you take the x^4 out of the 1/12x^4 tho

to get (1/12)x^-4

because the - makes it reciprocal

[sullen breach]

they're multiplied together

reciprocal doesnt apply here

[jade adder]

yeah so take the x out

[sullen breach]

if you were trying to do ur method

it would be 12x^-4

but that still doesnt work

because thats applied on the 12 not the x

[jade adder]

isnt 1/12x^4 the same as (1/12)x^-4

my teacher said always do that

take the x out

[sullen breach]

i dont know what ur teaching is saying

because

the power rule consists of x^n -> nx^n-1

which means u multiply ur coefficient by ur power

and then reduce power by 1

for example

[jade adder]

@willow granite how do you do it

[sullen breach]

x^3 goes to 3x^2 as u multiply the entire thing by 3 and reduce power by 1 so 3 goes to 2

[jade adder]

yeah i know that

but say you had y = 2/3x^2

youd make that y = (2/3)x^-2

[sullen breach]

are u saying 2/ 3 x^2

or 2/(3x^2)

[jade adder]

y = 2/(3x^2)

thatd be (2/3)x^-2

to get dy/dx = -4/3x^3

[sullen breach]

hold up

this may be a print error

it seems like the x^4 is on the denominator

however the fraction line doesnt extend that long

[jade adder]

should i just email my teacher

[sullen breach]

ive done the other way

it doesnt seem like that is correct

email ur teacher to question if this is a print error

because if it was how u said u would get an answer of 6th root of 5/147

which seems not correct

im betting the answer is 7

[jade adder]

im currently on 5/(3x^6) = 55

[iron surge]

X^4 is on the numerator, remember the question from my real fm gcse exam

[rugged tide]

(1/12)x⁴ + 3x² + 4
dy/dx = 1/3x³+6x
d²y/dx²= x²+6
x²+6=55
x²+6-55=0
(x+11)(x-5)=0
x=-11
x=5

positive
so x=5

[jade adder]

Yo @sullen breach you were right, it was a misprint good job on spotting that

[rugged tide]

it can't be x⁴ on the denominator, would be too difficult

[jade adder]

Yeah it’s (1/12)x^4

[sullen breach]

bro?

x^2 + 6 - 55

not x^2 - 6x - 55

[rugged tide]

oh lol

7 then

[sullen breach]

lmao