VCE Methods Question Thread!

[monkeywantsabanana]

Consider the graph y=xe^x

Is it correct to say that there's an asymptote at y=0? or do you have to say that y=0 for values of x<0?

[pi]

I think saying y=0 (ie. when labeling the asymptote on a sketched graph) is sufficient at a Methods level, as the latter is implied

[Kelui]

Any idea?

"Use the following data to create a polynomial that will model the information given.

1) f(-1)=0 and f(4)=0

a. f'(2)=0 and f'(x)>0 for x<2 and f'(x)<0 for x>2 -(not sure if that is the right order)

Sketch a simple graph that will model the information above. (3 marks)"

[Phy124]

f(-1)=0

Is this supposed to be f(0)=0

f(4)=0

Or alternatively, this f(5)=0, by any chance?

It appears they are looking for a negative parabola with a turning point in the positive part of the y axis, but unfortunately this can't be done with the information given, as the turning point won't be halfway between the x-intercepts.

[breadkay]

Just wondering what is the best way to solve an equation like:

[kamil9876]

Let and then you really want to solve

[pi]

Just wondering what is the best way to solve an equation like:

  (times both sides by )

Let




edit: beaten...

Yep, you can do the rest

[breadkay]

Thank you, thank you! 

I did the substitution method as above, but didn't think to multiply out

[AutumnConcerto]

I have a question regarding differentiating a modulus function!

lets just say f(x) = |x^2-1|

The textbook says that to differentiate this, you would define the function as:

f(x) = g(h(x)) where g(x) = |x| and h(x) = x^2-1, converting this into a composite function.

Then it says that by using the chain rule we can find the derivative of f(x) using the following formula:

f'(x) = g'(h(x))h'(x)
Its this part that I don't understand D:

Can anyone help out? Much appreciated

[kamil9876]

That is exactly the chain rule. Maybe not stated exactly as you know it.

[AutumnConcerto]

That is exactly the chain rule. Maybe not stated exactly as you know it.

Yeah thats what I don't understand -.-
Can you briefly explain how it is the chain rule? D:
What I was taught is dy/dx = du/dx x dy/dx, I wasn't taught the Leibniz notation.

[Phy124]

That is exactly the chain rule. Maybe not stated exactly as you know it.

Yeah thats what I don't understand -.-
Can you briefly explain how it is the chain rule? D:
What I was taught is dy/dx = du/dx x dy/dx, I wasn't taught the Leibniz notation.

Well you can do it using that notation but its a bit more messy IMO. (especially considering you might have to let , if you didn't already know the derivative of an absolute function)





^See this, if you don't understand why









Now to explain why , eh? <-- probably easier said than done

In reality what you have denoted as u is what the textbook has donated as h(x).

Lets say we had,

1.

2.

3.

4.

5.

Alternatively...



Make this

1.

2.

3.

4.

5.

Not sure you'll understand that, but hey, worth a shot

[AutumnConcerto]

That cleared up everything, thanks so much!
You were very concise so yeah i understood

[dinosaur93]

can someone be kind enough to help me walk through these questions? tnx heaps~!

Q1 c and d,
How do you show that one grpah touches the other?

[ecvkcuf]

Let y=ⁿ be a power function where n is a whole positive number, use calculus to find which values of n there is a local minimum of the function..

Don't really know how to approach this question.. do I just sub in a random positive number and then use calculus to find the stationary points and then the local minimum?

Please help.. please show all working out..


2)a) Consider the power function x^2/3 which is assumed to have relationship x^2/3=(x^1/3)² and this applies to all fractional indices

(i) Use calculus to show that the minimum of this function is a cusp and state its coordinates. (In this answer you expected to provide a definition of a cusp)

b) Consider y=x^4/3
i) Use calculus to investigate its minimum. Is it a local minimum or a cusp and state its coordinates.