Help with calculus pls | Mathematics | Page 1

olive rampart Mar 30, 2025, 8:19 PM

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Help😭

whole sparrowBOT Mar 30, 2025, 8:19 PM

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olive rampart Help😭

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olive rampart Mar 30, 2025, 8:19 PM

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Wait I think I'm cooking

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Nah I'm cooked gng

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Help

tardy prawn Mar 30, 2025, 8:26 PM

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Ok, so we know that the area of a rectangle is base times height

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So what variable represents the base of this rectangle, and which represents its height?

olive rampart Mar 30, 2025, 8:26 PM

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2-x

tardy prawn Mar 30, 2025, 8:28 PM

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Hold on can you explain how you got 2-x as one of the dimensions?

olive rampart Mar 30, 2025, 8:28 PM

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Wait I meant

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The opposite

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X-2

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?

tardy prawn Mar 30, 2025, 8:29 PM

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Where did the 2 come from?

olive rampart Mar 30, 2025, 8:30 PM

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Nvm

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The area is

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xy

tardy prawn Mar 30, 2025, 8:30 PM

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Yes!

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So we need the product of our x and y values to be as great as possible

olive rampart Mar 30, 2025, 8:31 PM

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Do you have e the answer to this question

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Cus I think inaccidentally found the area

tardy prawn Mar 30, 2025, 8:31 PM

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You want the answer?

olive rampart Mar 30, 2025, 8:32 PM

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Just to check initially

tardy prawn Mar 30, 2025, 8:32 PM

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K I'll plug some numbers into a calculator

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brb

olive rampart Mar 30, 2025, 8:32 PM

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Yea I got fried

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It's more bc idk whether to use integration or differentiation

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I've been trying to use both

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As well as gradient of the line

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That runs from 0,0 to x,y

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Then once I have that gradient

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I can find the equation

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Set the equations equal, find co ordinates

tardy prawn Mar 30, 2025, 8:34 PM

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Ok here

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What you want to do is find the coordinates where the product of x and y is the greatest, hence which will give the greatest area of a rectangle

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Makes sense?

olive rampart Mar 30, 2025, 8:35 PM

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Yes

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So u differentiate?

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Wouldn't that just be 1

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For x

tardy prawn Mar 30, 2025, 8:35 PM

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Maybe

olive rampart Mar 30, 2025, 8:36 PM

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Then y = 7

tardy prawn Mar 30, 2025, 8:36 PM

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But we cant be sure because you might have a small y value at x = 1

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Giving us a small area

olive rampart Mar 30, 2025, 8:36 PM

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Yes

tardy prawn Mar 30, 2025, 8:36 PM

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So let's say xy = area

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We know that y = 8 - x^3

dawn siren Mar 30, 2025, 8:38 PM

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olive rampart Help😭

the height will be (8-x^3), and the length will be x, so try to make an area formula based on that

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then maximize it

olive rampart Mar 30, 2025, 8:38 PM

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dawn siren the height will be (8-x^3), and the length will be x, so try to make an area for...

How do you know that's the height?

dawn siren Mar 30, 2025, 8:39 PM

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olive rampart How do you know that's the height?

because that is where the x-value line (i.e., x=c) will intersect the curve first

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let me draw it

olive rampart Mar 30, 2025, 8:40 PM

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Ye ik thay

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That

dawn siren Mar 30, 2025, 8:40 PM

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so the green segment is x (obviously)

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the red segment will be where x intersects the curve first

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any coordinate on y=8-x^3 can be represented as (x, 8-x^3)

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hence the above

olive rampart Mar 30, 2025, 8:41 PM

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dawn siren any coordinate on y=8-x^3 can be represented as (x, 8-x^3)

Is this a general rule?

dawn siren Mar 30, 2025, 8:41 PM

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olive rampart Is this a general rule?

yes

olive rampart Mar 30, 2025, 8:41 PM

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Ohh wait I see it now

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That y

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Is the same as the other y

dawn siren Mar 30, 2025, 8:42 PM

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yep

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since it is a rectangle

olive rampart Mar 30, 2025, 8:43 PM

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So the formula is

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8x-x⁴

dawn siren Mar 30, 2025, 8:44 PM

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yep

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A=8x-x^4, differentiate, find when A'=0, then make sure it is when 0<x<2

olive rampart Mar 30, 2025, 8:44 PM

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How is that an 8 marker

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There's like 4 lines of working out

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I got 7.56 as the max area

dawn siren Mar 30, 2025, 8:46 PM

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lol

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well there is one more thing

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check the endpoints and critical points

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and see which yields a max

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but other than that this is pretty easy

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,calc 8*cbrt(2)-(cbrt(2))^4

narrow oracleBOT Mar 30, 2025, 8:49 PM

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Result:

7.5595262993692

dawn siren Mar 30, 2025, 8:49 PM

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olive rampart I got 7.56 as the max area

yep

worn coyoteBOT Mar 31, 2025, 9:00 PM

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@olive rampart

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olive rampart Mar 31, 2025, 9:07 PM

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+close

worn coyoteBOT Mar 31, 2025, 9:07 PM

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olive rampart +close

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#Help with calculus pls