hey guys would like some help with f'(x)=x^2 root 12-8x not sure how to find the cutting point

[woven geyser]

What's a "cutting point"?

[dense flint]

thats what u call it in my language its like when the y reaches zero or something

[woven geyser]

So simply you are asking f'(x) = 0?

[dense flint]

like when y is (2,0)

[woven geyser]

y is a single value, not a point

[dense flint]

im having a strugle trying to find what it called mb

ill send a photo rq

i hope u understand it

[woven geyser]

wtf

[dense flint]

mb the y'(x) shouldnt be there

[woven geyser]

Can you answer this question, simply?

[dense flint]

no its not like that

thats what i mean

[woven geyser]

What does that line represent? The derivative or primitive?

[dense flint]

sorry for the struggle its not the derivative not sure what is primitive

[woven geyser]

If derivative f' then primitive is f

[dense flint]

but im trying to find when y hits 0

yea primitive

[woven geyser]

But then you have f'(x) = x²sqrt(12-8x)

You wanna find f(x) = 0 but you are given the derivative

Unless you did a typo

[dense flint]

dam i did a mistake mb

its primitive not a derivative

sorry

[woven geyser]

So you mean f(x)

instead of f'(x)

[dense flint]

yes

[woven geyser]

Ok

finally

[old pulsar]

𝔸dωn𝓲²s

[woven geyser]

You just need to apply Zero Product Theorem

[dense flint]

the answer i got was y= sqrt 12

[woven geyser]

A product is 0 if at least one of its factors is 0.

But first we need to check the domain, 12-8x >= 0 so 3/2 >= x

Check

x² = 0

and

sqrt(12-8x) = 0

[dense flint]

yea i got 3/2

[woven geyser]

ok good

there is another solution as well

[dense flint]

wait uh

how its called when y=0

like0,0

[woven geyser]

x-intercepts

roots

zeroes

[dense flint]

wait so how do i find the intercept i think for when y=0

then its 0=x^2 sqrt12-8x

[woven geyser]

You already found one

x = 3/2

and I am saying there is another one

[dense flint]

oh

wait so what i need to do sorry i didnt quite understand

[woven geyser]

read again

[dense flint]

so i need to solve both of them?

[woven geyser]

of course

What happens if ||x=0||?

[dense flint]

then its 0?

[woven geyser]

yea

so x = 0 and x = 3/2 are the x-intercepts s.t. y = 0

[dense flint]

wait so if its 0 then also y is 0? like then i got both intercepts?

[woven geyser]

yes

[dense flint]

i also found the derivative

its x=0 and x=1.2 which im not sure its true because 3/2

and it cant be

[woven geyser]

What

[dense flint]

i mean the when u comparing derivative to 0

then u get a number when the function is lowest or highest

[woven geyser]

First of all what is f'(x)?

How did you calculate it?

[woven geyser]

ok lol

[dense flint]

i did ratzional i think formula

[woven geyser]

,, f'(x) = 2x\sqrt{12-8x}-\frac{4x^2}{\sqrt{12-8x}}

[old pulsar]

𝔸dωn𝓲²s

[woven geyser]

Now you wanna know f'(x) = 0

,, 0 = 2x\sqrt{12-8x}-\frac{4x^2}{\sqrt{12-8x}}

[old pulsar]

𝔸dωn𝓲²s

[dense flint]

pretty sure its 8x^2

[woven geyser]

8/2?

[dense flint]

,, 0 = 2x\sqrt{12-8x}-\frac{8x^2}{\sqrt{12-8x}}

[old pulsar]

madrega

[dense flint]

like that

[woven geyser]

8/2=

?

[dense flint]

yea mb

,, 0 = 2x\sqrt{12-8x}-\frac{8x^2}{\sqrt2{12-8x}}

no wait

[woven geyser]

just delete bro

[dense flint]

2*sqrt12-8x

[woven geyser]

,, 2x\sqrt{12-8x}=\frac{4x^2}{\sqrt{12-8x}}

Now rearrange

[dense flint]

ohhh

[old pulsar]

𝔸dωn𝓲²s

[dense flint]

nah nvm im just dumb

,, 2x\sqrt{12-8x}=\frac{8x^2}{\2\sqrt{12-8x}

[old pulsar]

madrega
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[dense flint]

how do u multiply

[woven geyser]

Now assume x != 3/2 not equatl to 3/2

And then multiply by sqrt(12-8x)

,, 2x(12-8x) = 4x^2

[old pulsar]

𝔸dωn𝓲²s

[woven geyser]

Now bring everything to one side and factor 2x

,, 4x^2-2x(12-8x) = 2x(2x-(12-8x))=0

[old pulsar]

𝔸dωn𝓲²s

[woven geyser]

Now again zero product theorem

[dense flint]

i think u messed up a lil

its 8x^2

[woven geyser]

2x = 0 or 2x-(12-8x) = 0

[dense flint]

i got x=0 or x=1.

[woven geyser]

How did you get x=1?

[dense flint]

1.2

[woven geyser]

ok correct

[dense flint]

wait

[dense flint]

did u divide it?

like u can do that?

[woven geyser]

I multiplied it assuming x is not 3/2

[dense flint]

oh alright

wait so now i got enough info to sketch the function?

[woven geyser]

You would need to verify if these are actual extreme values but yea you can try

You could try to anaylize the limits towards x->-inf

[dense flint]

but this arent but x>=3/2?

[woven geyser]

wdym

[dense flint]

i mean we found domain right?

[woven geyser]

yes

what happens for very small values of x

[dense flint]

so if x>=3/2

[woven geyser]

no

[dense flint]

how can x be 0 or 1.2

[woven geyser]

x <= 3/2

[dense flint]

oh

so to verify it i need to check values in the original function or the premitive?

[woven geyser]

No

You do either 1st derivative test (Is there a change of monotony) or 2nd derivative test.

[dense flint]

yea the first test

thats also how u sketch the premitive right?