maths homework due in 6 hours

[paper thicket]

🙏🏼

[radiant wave]

1. Do not ping the Moderators, unless someone is breaking the rules.
2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
3. Do not ping other members randomly for help.
4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
5. Wait patiently for a helper to come along.
6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[honest prairie]

what have you tried?

[paper thicket]

ive found the second deriv

i just dont understand the question

havent practiced finding concave

i got 24x^2-22

[honest prairie]

that feels incorrect

[paper thicket]

ah

what do you make it?

[honest prairie]

do you know when a graph is concave?

[paper thicket]

no

[honest prairie]

i got a different answer to you

[paper thicket]

you are most likely right lol im struggling in school

[honest prairie]

a concave graph is where the gradient is decreasing

in other words, the second derivative is negative

[paper thicket]

convex is increasing and concave decreasin

would second deriv be y=24x^2-22

because its f(x)??

[balmy temple]

no, not necessarily.

[paper thicket]

ah

[balmy temple]

you're missing a term.

specifically speaking, an x term.

remember, f(x)=2x^4-11/x^3/3-5x^2

[paper thicket]

ah ok so 24x^2-22x-10

?

=y?

or am i completly wrong here?

[balmy temple]

yes, this is right

[paper thicket]

i dont want to waste your time if im just not getting it

[paper thicket]

sweet

[balmy temple]

you are not wasting my time

i am wasting my own time

[paper thicket]

lmao

[balmy temple]

i chose to waste my time

not your fault

[paper thicket]

fair enough

atelast its something ish productive

[honest prairie]

additionally: it’s not wasting time if you enjoy it

[balmy temple]

i guess

[paper thicket]

now that i have f(x)=24x^2-22x-10 where do i go from here

use values of x

and find ys?

[balmy temple]

determine where its greater and less than zero

[paper thicket]

and then get gradients?

[honest prairie]

recall the definition of concavity

[paper thicket]

gradient is decreasing

[balmy temple]

because concave up -> f''(x) is positive

concave down -> f''(x) is negative

[honest prairie]

yes, so the second derivative that you obtained should be negative

[honest prairie]

i think they’re using concave and convex

[paper thicket]

does that mean f"(x) would be convex?

since inverse func?

[honest prairie]

no

[paper thicket]

aw

[balmy temple]

whar

convex?

[paper thicket]

i got no clue

ill just try and follow this question before i try and think about other things

[paper thicket]

to do this do i test values of x and find what point y turns from negative to positive using integers?

[balmy temple]

solve the inequalit

y

24x^2-22x-10>0 and <0

[paper thicket]

ok

so i factorise and get x values?

[balmy temple]

yeah, then solve inequality

[paper thicket]

ok

when using 5/4 as my x value i got 0

and when using -1/3 as my x value i got 0

im a bit confused

[balmy temple]

ye

[paper thicket]

because surely its meant to give either a positive or negative value to satisfy the inequality?

[balmy temple]

so we have 2(4x-5)(3x+1)>0 and <0

therefore

[paper thicket]

ahhh

i forgot to have the 2 in the (6x+2)

[balmy temple]

use regual quadratic inequality methods

wait

mistyped

there

[paper thicket]

i use quadratic formula?

[balmy temple]

no

[paper thicket]

oh

[balmy temple]

ok lets say its >0

then $x>r_1$ and $x<r_2$ where $r_k$ are the roots of the quad

[pseudo sphinx]

dark matter

[balmy temple]

you gotta determine which one is which

for <0 its $r_1<x<r_2$

[pseudo sphinx]

dark matter

[paper thicket]

so i write it as 24x^2 < -22x< -10 ??

im not just messing about i js genuinly dont get it lol

i follow so far

js this bit i dont understand

[paper thicket]

this is y<0

which is the concave part im looking for?

wait no i want both

i need to show its concave and not just one part of the graph right?

ill watch a quick video on it and see if it helps

i understand this now

[balmy temple]

good

[paper thicket]

convex up is anticlockwise movement and concave down is clockwise movement

ik it can probably be flipped so that might not always be true

but for this example

so im trying to prove my equation follows that pattern between a certain region?

so the "x" >< is capturing the point of the graph where it is concave??

[balmy temple]

ye

[paper thicket]

so i have f(x)= 24x^2 -22x -10 >0 and f(x)= 24x^2 -22x -10 <0

is the points i need

which is effectivly the two black dots on the graph?

i think i understand maybe ill try it

will my two black dots on my graph have coordinates (-1/3,0) and (5/4,0)??

[balmy temple]

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

[paper thicket]

i feel so brain dead

this is probably so painful for you😭

[balmy temple]

1d20h9

brain matter decomposing...

[paper thicket]

go sleep bruh

[honest prairie]

it's fairly accurate, i think (but you're mixing notation a little bit)

[honest prairie]

you should sleep

[honest prairie]

it's alright

[paper thicket]

is this correct do you know??

guessing the question is asking about the line inbetween these points i feel like the coords are wrong

[honest prairie]

if you only want the part where the graph is concave, it should just be the <

[paper thicket]

because its a decreasing gradient?

[honest prairie]

yes, so a negative second derivative

[honest prairie]

x = -1/3 and x = 5/4 are where f"(x) = 0, yes

[paper thicket]

ah ok so if the second deriv is 24x^2-22x-10 do i just flip the symbols ??

[honest prairie]

hm?

[paper thicket]

so i have f(x)= -24x^2 +22x +10<0

??

oh

[honest prairie]

you have 24x^2-22x-10 < 0

[paper thicket]

did you mean the second deriv gives a negative result?

[paper thicket]

ye

[honest prairie]

yes

[paper thicket]

ok mb

[paper thicket]

where do i go from here or is this just the answer?

because it shows that the gradient is decreasing?

[honest prairie]

ideally you would now solve for the range of x

[paper thicket]

do you mind showing me this??

just dont have any idea on how to start

[honest prairie]

24x^2-22x-10 < 0
do you know how to factor the left hand side?

[paper thicket]

yes

gives me values of x as 5/4 and -1/3

[honest prairie]

that's solving 24x^2-22x-10 = 0, but sure

[paper thicket]

oh

[honest prairie]

when would it be smaller than 0?

[paper thicket]

no

it would =0?

or am i wrong

cause i plug that into the equation?

[paper thicket]

I DID IT

concave up=(-∞,-1/3) u (5/4,∞)

concave down= (-1/3,5/4)

i think anyway

[honest prairie]

yes, sorry, i went offline

these look correct

[paper thicket]

whooooo

i completed all my maths homework

this is the whole sheet if you were curious probably not but still

also idk how to close this since im not on the server often

[honest prairie]

type +close

[paper thicket]

but mods can close this now🙏🏼

ah ok

[honest prairie]

then hit some blue buttons (optional) and the red button

[paper thicket]

+close

[noble spruce]

Please thank your Helpers before closing!

Please thank the helpers who assisted you by clicking the buttons below. You can thank each helper only once. Once you're done, click "Close Post" to close this thread.

[noble spruce]

Thank you for your feedback! half the folk has been awarded 1 . They now have 50 . They have 2 daily left for today.

[noble spruce]

Thank you for your feedback! dark matter has been awarded 1 . They now have 42 . They have 2 daily left for today.