Calculus | Mathematics | Page 1

undone linden Dec 1, 2023, 4:50 AM

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Im confused how to solve this

twilit gazelleBOT Dec 1, 2023, 4:50 AM

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undone linden Im confused how to solve this

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limber light Dec 1, 2023, 4:53 AM

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Mm i prefer logarithmic differtiation

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That will simplify your answer

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Btw you have to use product rule

undone linden Dec 1, 2023, 4:54 AM

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i have not learned that,

undone linden Dec 1, 2023, 4:54 AM

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limber light Btw you have to use product rule

i dont see 2 terms

limber light Dec 1, 2023, 4:55 AM

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X and root 900-x

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Two dif terms

undone linden Dec 1, 2023, 4:55 AM

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but thats chain rule

limber light Dec 1, 2023, 4:55 AM

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No its product rule

undone linden Dec 1, 2023, 4:56 AM

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but the 900-x has the power of 1/2

limber light Dec 1, 2023, 4:56 AM

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That is chain rule

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But first you have to aply product rule

undone linden Dec 1, 2023, 4:57 AM

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that looks like an overload profile picture

limber light Dec 1, 2023, 4:57 AM

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Oh yes i drew it

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If you know log i can teach you a more elegant method

undone linden Dec 1, 2023, 4:58 AM

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limber light

im not sure i understand, i thought of the terms givin as chain rule becasue of the squre root

undone linden Dec 1, 2023, 4:58 AM

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limber light If you know log i can teach you a more elegant method

i dont]\

limber light Dec 1, 2023, 4:59 AM

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Oh ok

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So here x is one function dependent on the variable and root of 900 -x is one more function

undone linden Dec 1, 2023, 5:00 AM

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there is no way we use product rule

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can't be

limber light Dec 1, 2023, 5:00 AM

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undone linden Dec 1, 2023, 5:02 AM

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can we do it with chain rule?

limber light Dec 1, 2023, 5:02 AM

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No chain rule is different

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When you do d/dx of f(x) you use chain rule

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Chain rile is only when there is one function that is complex

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So now try using this

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And find the answer

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I will wait

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Any problems?

undone linden Dec 1, 2023, 5:07 AM

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yes,

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well i was doing side research on chain rule rq to try and figure stuff out

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it honestly does look like I can do chain rul e

limber light Dec 1, 2023, 5:08 AM

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No

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Its not like chain rule

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In chain rule a function is inside another function

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Like 900-x a function is inside a root function

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X on the other hand is not

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It is just multiplied

undone linden Dec 1, 2023, 5:10 AM

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, are you trying to say x represents its own term making x and the squarroot functino only differntiable with product rule

limber light Dec 1, 2023, 5:10 AM

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Yep

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Soooo got the answer?

undone linden Dec 1, 2023, 5:18 AM

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one sec

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yeah i couldn't

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limber light Dec 1, 2023, 5:24 AM

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You made a slight mistake

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In second part it is -x

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900-x

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@undone linden

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Then you just equate to zero and you will get correct answer

undone linden Dec 1, 2023, 5:25 AM

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limber light In second part it is -x

where?

limber light Dec 1, 2023, 5:25 AM

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Like you wrote 900+x

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Instead of 900-x

undone linden Dec 1, 2023, 5:25 AM

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ohhh

undone linden Dec 1, 2023, 5:26 AM

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limber light Then you just equate to zero and you will get correct answer

like i make f(x) = to 0?

limber light Dec 1, 2023, 5:27 AM

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Derivate is equal to zero as they are asking to find maxima

limber light Dec 1, 2023, 5:27 AM

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undone linden

This equal to 0

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Here i am saying

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Mm do you habe any question?

undone linden Dec 1, 2023, 5:35 AM

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isolate for x i assume but that seems like a long process

limber light Dec 1, 2023, 5:36 AM

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No it is not

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Very simple

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Let me show you

undone linden Dec 1, 2023, 5:37 AM

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it does seem hard

limber light Dec 1, 2023, 5:37 AM

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Nah its just 2 step process

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I elaborated it so that you can understand the steps

undone linden Dec 1, 2023, 5:42 AM

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interesting

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so the (900 - x) cancel out

limber light Dec 1, 2023, 5:42 AM

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Not cancel out

undone linden Dec 1, 2023, 5:43 AM

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well\

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combine

limber light Dec 1, 2023, 5:43 AM

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Yep

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Its like √x*√x

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=x

undone linden Dec 1, 2023, 5:43 AM

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yep

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alright and then after i get my x, which is 600

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whats next?

limber light Dec 1, 2023, 5:45 AM

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Just input the value in pi of x

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Cause you found value at which it is max

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Now you have to find the maximum value

undone linden Dec 1, 2023, 5:48 AM

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ah

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we solved for x

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so jus plug x back in and find profit

limber light Dec 1, 2023, 5:49 AM

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Yep

undone linden Dec 1, 2023, 5:49 AM

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nice, thank you

limber light Dec 1, 2023, 5:50 AM

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Just tell me the final answer so i can cross check it

undone linden Dec 1, 2023, 5:50 AM

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A

limber light Dec 1, 2023, 5:51 AM

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Yeah ok nice

undone linden Dec 1, 2023, 5:51 AM

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also

limber light Dec 1, 2023, 5:52 AM

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Just sp you know here is an elegant way of solving

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undone linden Dec 1, 2023, 5:53 AM

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natural logs instead of logs?

limber light Dec 1, 2023, 5:53 AM

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Without any chain rule product rule

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Yeah cause differentiation

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Of ln x is 1/x

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We dont need any extra terms like base and all

undone linden Dec 1, 2023, 5:55 AM

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yeah

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you are right

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does log differnetiaon work with all problems?

limber light Dec 1, 2023, 5:57 AM

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It is suitable for those with many functions multiplied

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Some case implicit is better

undone linden Dec 1, 2023, 5:58 AM

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i see

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also

#Calculus