Calculus max min real life problem | Mathematics | Page 1

buoyant socket Mar 19, 2024, 4:18 AM

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The highlighted qs 3 please

plucky pendantBOT Mar 19, 2024, 4:18 AM

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buoyant socket Mar 19, 2024, 4:19 AM

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i don’t understand the highlighted part

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these r solutions btw

young hedge Mar 19, 2024, 8:53 AM

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buoyant socket these r solutions btw

Imagine you got sin(something)

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What is the maximum value you can get from that sine?

buoyant socket Mar 19, 2024, 9:19 AM

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young hedge What is the maximum value you can get from that sine?

pi/2?

young hedge Mar 19, 2024, 9:19 AM

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Just generally the max value of sin(x)

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Not x

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The value of sin(x)

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Do you agree that sine is in between 1 and -1?

buoyant socket Mar 19, 2024, 9:20 AM

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yep

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1?

young hedge Mar 19, 2024, 9:20 AM

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Exactly!

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The solution is trying to tell you that no matter what is inside the sine, the max value would
sin(pi/2) (or as you just said 1)

buoyant socket Mar 19, 2024, 9:21 AM

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So it will always be 1?

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The max value?

young hedge Mar 19, 2024, 9:22 AM

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Yes the max value of sine is 1

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Also one thing

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What if I ask what is the max value of sin(x) + 3?

buoyant socket Mar 19, 2024, 9:22 AM

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it’s 3?

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Oh 4

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Wait idk

young hedge Mar 19, 2024, 9:22 AM

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Yes!

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Exactly

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4 is the max value

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Since if sin(x) is 1

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You would get 4

buoyant socket Mar 19, 2024, 9:23 AM

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ohhh ok

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I get it thank you @young hedge

young hedge Mar 19, 2024, 9:23 AM

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No problem

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But sorry not to be annoying

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Let me give you some other examples

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So I can be sure you get it

buoyant socket Mar 19, 2024, 9:24 AM

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young hedge But sorry not to be annoying

no worries, I’d like that

young hedge Mar 19, 2024, 9:24 AM

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Ok nice

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What is the max value 2sin(x)

buoyant socket Mar 19, 2024, 9:24 AM

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2?

young hedge Mar 19, 2024, 9:24 AM

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Exactly!

buoyant socket Mar 19, 2024, 9:24 AM

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yay

young hedge Mar 19, 2024, 9:24 AM

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What about
3sin(x) + 5

buoyant socket Mar 19, 2024, 9:24 AM

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8?

young hedge Mar 19, 2024, 9:24 AM

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Yep!

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This one is tricky!

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Try not to fall in the trap

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-sin(x) + 1

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Max value

buoyant socket Mar 19, 2024, 9:25 AM

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2?

young hedge Mar 19, 2024, 9:26 AM

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Damn

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Yes!

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That's correct

buoyant socket Mar 19, 2024, 9:26 AM

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Yay

young hedge Mar 19, 2024, 9:26 AM

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Ok one more

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sin(2x^2 + 3x - 5)

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Max value

buoyant socket Mar 19, 2024, 9:26 AM

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woah what

young hedge Mar 19, 2024, 9:27 AM

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You don't even have to touch inside of the sine!

buoyant socket Mar 19, 2024, 9:27 AM

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this is hard

young hedge Mar 19, 2024, 9:27 AM

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Well in fact

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Let's say
2x^2 +3x -5 = A

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If I had asked you

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The max value for sin(A)

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What would you say?

buoyant socket Mar 19, 2024, 9:28 AM

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1?

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Uh

young hedge Mar 19, 2024, 9:28 AM

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And guess what!

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That's the answer

buoyant socket Mar 19, 2024, 9:28 AM

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It’s 1?

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Oh yay

young hedge Mar 19, 2024, 9:28 AM

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Yep

buoyant socket Mar 19, 2024, 9:29 AM

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wait why

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So no matter what’s in the bracket

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it’s max value is 1? If it doesn’t change its amplitude or if it’s not vertically shifted?

young hedge Mar 19, 2024, 9:29 AM

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Yep exactly!

buoyant socket Mar 19, 2024, 9:29 AM

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ohhh okay

young hedge Mar 19, 2024, 9:30 AM

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Well the designer of the question can make it tricky by limiting the range of the thing inside the sine

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But for now

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Just know that the max value for sine is 1

buoyant socket Mar 19, 2024, 9:30 AM

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yep thank you 🙏🏼

young hedge Mar 19, 2024, 9:30 AM

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Also everything we just discussed

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Applies to cosine as well!

buoyant socket Mar 19, 2024, 9:31 AM

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ahhh ok

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what about tan

young hedge Mar 19, 2024, 9:31 AM

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Well as you know tan can give any value

buoyant socket Mar 19, 2024, 9:31 AM

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oh shoot ur right

young hedge Mar 19, 2024, 9:31 AM

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Yeah

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We are done I think

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You can close the forum if you want

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I will send an example of how a question designer can make the max value of sine not be 1

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So you can get the idea

buoyant socket Mar 19, 2024, 9:32 AM

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this has been very helpful I appreciate it

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ok

young hedge Mar 19, 2024, 9:33 AM

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Happy to hear that

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You can close the forum after I send the problem

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For now cya later!

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(I mean i will send it after like 20 minutes or something)

buoyant socket Mar 19, 2024, 9:34 AM

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cya

young hedge Mar 19, 2024, 9:52 AM

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buoyant socket cya

turned out to be a little too hard

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I gotta go rn, try to think about for a while

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It is asking for the max value of sin(cos(x)*pi)

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IN THE INTERVAL MENTIONED

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This is a type of question where the max value is not 1

buoyant socket Mar 19, 2024, 10:07 AM

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I have no idea

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0?

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I used coordinates tho, not sure how else to do this

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Damn

buoyant socket Mar 19, 2024, 10:40 AM

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wait this is a guess but

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The max value of cos(x) between pi/2 and pi is 0

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And sin(0 times pi) equals to zero

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so 0?

young hedge Mar 19, 2024, 11:34 AM

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buoyant socket so 0?

YES!

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That is correct!

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And the minimum point is -1

buoyant socket Mar 19, 2024, 11:40 AM

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YAYY

young hedge Mar 19, 2024, 1:52 PM

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buoyant socket YAYY

we are done

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you can close the forum if you want

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Cya!

buoyant socket Mar 19, 2024, 5:58 PM

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cyaa

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.close

#Calculus max min real life problem