ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: lisafaustina on October 28, 2010, 02:23:55 pm

Title: quick question on slope fields
Post by: lisafaustina on October 28, 2010, 02:23:55 pm

just say we get a slope field in multiple choice and you have to pick one of 5 equations or whatever, do you have to pick the equation representing the graph the slope field is showing or the antiderivative of the graph the slope field is showing?
its sooo confusing
also what do they mean when they say first-order or sometihng like that

Title: Re: quick question on slope fields
Post by: jasoN- on October 28, 2010, 02:26:47 pm

you pick the equation showing the derivative of the graph, if the graph is y versus x

Title: Re: quick question on slope fields
Post by: lisafaustina on October 28, 2010, 04:22:10 pm

Um ok so what if the graph is dy/dx

Title: Re: quick question on slope fields
Post by: theuncle on October 28, 2010, 04:25:00 pm

A slope field is the graph of a differential equation. First order means it only involves dy/dx. The graph will always be y vs x, and the equation will always involve dy/dx
Also, it's not about finding an antiderivative, sometimes you can't. It's about recognising what the gradient is at a point by using the differential equation

Title: Re: quick question on slope fields
Post by: lisafaustina on October 28, 2010, 04:27:25 pm

I still don't get it. So if they show you a slope field that is y vs x and it shows like a cubic graph or something, do you pick the equation that is a quadratic or a quartic? Someone give me an example ><

Title: Re: quick question on slope fields
Post by: 98.40_for_sure on October 28, 2010, 04:28:52 pm

I recommend you to just test points into your solutions, it's so much quicker and impossible to get it wrong.

Title: Re: quick question on slope fields
Post by: theuncle on October 28, 2010, 04:31:03 pm

If they give you a graph that looks like a cubic, then the function is a cubic. hence, dy/dx =x^2+c, this is the differential equation. Relying on differentiation to work out the equation is a bad move, as 99.95 said it's always best to test points

Title: Re: quick question on slope fields
Post by: TrueTears on October 28, 2010, 04:49:32 pm

Quote from: 99.95_for_sure on October 28, 2010, 04:28:52 pm

I recommend you to just test points into your solutions, it's so much quicker and impossible to get it wrong.

this

Title: Re: quick question on slope fields
Post by: lisafaustina on October 28, 2010, 04:54:02 pm

What exaclty are they asking you when they give you the graph?

Title: Re: quick question on slope fields
Post by: SixWinged on October 28, 2010, 04:57:20 pm

Pretty sure they always state that they are looking for "The differential equation", in which case you write dy/dx = ....
In the case of multiple choice I'm pretty sure they occasionally don't mention the words "differential equation specifically, but all the answers are written as: "dy/dx = ...." so it's pretty obvious.

VCAA aren't looking to trick you by hiding things like this, if you read the question properly there shouldn't be any trouble interpreting what it is asking for.

Title: Re: quick question on slope fields
Post by: jasoN- on October 28, 2010, 04:58:00 pm

most likely the differential equation (ie. dy/dx = ..)
so when they give you a graph of function y consisting of a family of curves, you need to use those curves to find out what the derived function is
as a 'slope' field essentially measures the gradients of a function (correct?)

Title: Re: quick question on slope fields
Post by: Elnino_Gerrard on October 28, 2010, 07:03:25 pm

SKetching slope fields is a bitch though.like in the 07 when they tell u to draw that tan graph.  :'(