MAXIMUMS! Urgent Help Please (1 Viewer)

[*Ninny-mole*]

Okay with less thn 12 hours until the frigon maths HSC, I am getting worried about the fact I still don't understand maximums. Not the types of st. points, but when they ask find the max volume, or the max amount of something. I do not know what to do. Please help me.....I'm uber desperate right now.

 

[Riviet]

Follow 3 simple steps:

1) Differentiate with respect to the other variable that you are not finding the maximum of.

2) Let this derivative equal zero and solve for the variable.

3) To find the max "insert object here", substitute the answer found in 2) into your original equation or function that you differentiated.

Note: Strictly speaking, you need to also prove that it's a maximum either using first or second derivative test.

Also: you can use this same procedure for finding a "minimum"

 

[vanush]

Okay with less thn 12 hours until the frigon maths HSC, I am getting worried about the fact I still don't understand maximums. Not the types of st. points, but when they ask find the max volume, or the max amount of something. I do not know what to do. Please help me.....I'm uber desperate right now.

It's the same principle. They just make the volume or 'amount' of something into a mathematical function. As you would do finding stationary points, you have to differentiate it then let f'(x) = 0 to find x.

However when you find x, you need to show whether it makes f(x) its maximum or minimum value. You can do this by finding f''(x) then subbing in x.

If f''(x) > 0, f(x) is concave up at x (minimum)

If f''(x) < 0 f(x) is concave down at x (maximum).

 

[SoulSearcher]

Usually, you follow a series of steps:

- Find out what quantity you are looking for, and find an expression for this quantity.
- Then get this expression down into the form of one variable, so for example if you have x² + xy, where y = x-1, get it down to terms of one varible only, in this case x, so you would have x² + x(x-1) = 2x² - x.
- Find the derivative of this expression, and find when the derivative is equal to 0 in that expression, so in the previous example, the derivative would be 4x - 1, and the value of x to make it 0 would be 1/4.
- Then find out the nature of the point, either by testing points on either side of the point or using the second derivative, in any case for a minimum the second derivative would be > 0 and for a maximum the second derivative would be < 0.
- Once you find out the nature of the turning point, substitute it into the original equation to find the maximum or minimum area, volume, whatever you are trying to find out.

Hope that helps a bit

 

[*Ninny-mole*]

Thanks so muchly, this really helps.

 

[airie]

A global maximum is the point where the function achieves its greatest value for all x values in the domain, and similarly for a global minimum, the least. You'd probably be required to find the global maximum/minimum within its domain or within part of its domain, where you'd just find all the local maxima/minima and compare with the function values at the boundaries of the domain. And in the case where the function is ever increasing/decreasing over an open interval, no global maxima/minina would exist respectively.