Minima and Maxima questions... who has the hardest one and how to solve it?

[olivercutbill]

Minima and Maxima questions are often difficult, but there are super easy ones too (the classic cylinder one). Does anyone have a general method which helps in solving these?

[jamonwindeyer]

Minima and Maxima questions are often difficult, but there are super easy ones too (the classic cylinder one). Does anyone have a general method which helps in solving these?

Hey Oliver! The method can be generalised into 3 steps:

1 - Form Two Equations with Three Variables
2 - Use Elimination to Remove One of These Variables
3 - Differentiate to Find the Maxima/Minima

Most maxima/minima questions follow this broad process. Sometimes they will lead you through Steps 1-2, or even give you the result you need to prove in the question, but the third step is always the same.

Getting good at these is all about practice! 

PS: Common mistake, don't forget to actually prove that what you've found is the maxima/minima you are after using the second derivative test (or equivalent)!

[jazza47]

Someone please help me with this ??

[jamonwindeyer]

Someone please help me with this ??

The working looks good to me on cursory glance! What's up? 

[RuiAce]

Someone please help me with this ??

[jamonwindeyer]

They are using the check method (check either side and in between the intercepts) instead of the graphic method, but I assumed that line was a dictation error since everything else is sweet  is there a particular question you had jazza47?

[RuiAce]

They are using the check method (check either side and in between the intercepts) instead of the graphic method, but I assumed that line was a dictation error since everything else is sweet  is there a particular question you had jazza47?

Yeah true, guess and check is fine. But if you wanted to indicate so it's better to skip the intermediate line anyway and jump straight to the number line.

[jazza47]

I don't know if it should be greater than or equal to OR just greater than

[RuiAce]

I don't know if it should be greater than or equal to OR just greater than

That's something that can be easily overlooked without hinting us to it, sorry

[olivercutbill]

Hey Oliver! The method can be generalised into 3 steps:

1 - Form Two Equations with Three Variables
2 - Use Elimination to Remove One of These Variables
3 - Differentiate to Find the Maxima/Minima

Most maxima/minima questions follow this broad process. Sometimes they will lead you through Steps 1-2, or even give you the result you need to prove in the question, but the third step is always the same.

Getting good at these is all about practice! 

PS: Common mistake, don't forget to actually prove that what you've found is the maxima/minima you are after using the second derivative test (or equivalent)!

OK that is a good general process. Thank you!