VCE Methods Question Thread!

[Quantum44]

Hi,
What is the simplest method to use to sketch sine and cosine graphs with translations?
Thanks

Solve the equation for x-intercepts and find average, highest and lowest y values then use general shape to sketch

Or

Sketch general shape without horizontal translations in a dotted line, then apply horizontal translations and translate all original points

[geminii]

How would I go about doing this question?

State the transformations required to map the graph of y = f(x) onto the graph of y = f(x-h)+k. If there is a turning point at (3,5), find all possible values of h and k.
NOTE: f(x) = (x+1)^2(x-1) or x^3 + x^2 - x - 1.

[zhen]

How would I go about doing this question?

State the transformations required to map the graph of y = f(x) onto the graph of y = f(x-h)+k. If there is a turning point at (3,5), find all possible values of h and k.
NOTE: f(x) = (x+1)^2(x-1) or x^3 + x^2 - x - 1

So x=-1 and x=1/3 are the x-coordinates of the turning points


So, the turning points are (-1,0) and (1/3,-32/27)
So, h=4 and k=5 or h=8/3 and k=167/27

This is what I got, but it might be wrong. Someone should correct me if I made a mistake.

[geminii]

Thanks zhen,
I understand your working out but I'm not sure how you got this from your working?

So, h=4 and k=5 or h=8/3 and k=167/27

[zhen]

Thanks zhen,
I understand your working out but I'm not sure how you got this from your working?

You need to get the turning points (-1,0) and (1/3,-32/27) to (3,5). h and k are positive horizontal and vertical translations. So basically I do (-1+h,0+k)=(3,5) and (1/3+h,-32/37+k)=(3,5) and solve for h and k.

[TheCommando]

For the function f with domain [0,2pie] f(x)=cos(x-pie/3)
When sketching the graph how do u know the min volume is -1
Is it because there is an invisible 1 in front of the bracket right?

[zhen]

For the function f with domain [0,2pie] f(x)=cos(x-pie/3)
When sketching the graph how do u know the min volume is -1
Is it because there is an invisible 1 in front of the bracket right?

Yea basically it's because the amplitude is 1 since it's 1cos(x-pi/3). If it was 2cos(x-pi/3) the min would be -2.

[QueenSmarty]

Can I please get some help with this question?:
Using the product rule, find the derivative with respect to x for: x^-3(x^3-4)^2.
I keep getting the answer as 3/x^4(x^3-4)(2x^2-x^3+4), however the answer is 3/x^4(x^6-16)

[zhen]

Can I please get some help with this question?:
Using the product rule, find the derivative with respect to x for: x^-3(x^3-4)^2.
I keep getting the answer as 3/x^4(x^3-4)(2x^2-x^3+4), however the answer is 3/x^4(x^6-16)

I find it easier to expand the second part, so that I don't have to apply chain and product rule. This is how I did it. Hope it helps. 

[A TART]

"Find two quadratic functions f and g such that f(1)=0 , g(1)=0 and f(0)=10, g(0)=10 and both have a maximum value of 18."

I've only been able to get this far......

f(x)=k(x-1)(x+a)

g(x)=k(x-1)(x+a)

I tried to use the general form and then find the values through simultaneous equations but in both cases I'm missing a piece of information... (I think it's something to do with with the vertex when y=18, but I'm not sure how to find the x value for it).

[Sine]

"Find two quadratic functions f and g such that f(1)=0 , g(1)=0 and f(0)=10, g(0)=10 and both have a maximum value of 18."

I've only been able to get this far......

f(x)=k(x-1)(x+a)

g(x)=k(x-1)(x+a)

I tried to use the general form and then find the values through simultaneous equations but in both cases I'm missing a piece of information... (I think it's something to do with with the vertex when y=18, but I'm not sure how to find the x value for it).

[LPadlan]

the point on the urve defined by the equation y=(x+3)(x-2) at which the gradien is -7 has coordinates:

[deStudent]

To find the maximum interval where f(x) is strictly increasing or decreasing, why do we include the value of x where a stationary/s point is?

[Shadowxo]

the point on the urve defined by the equation y=(x+3)(x-2) at which the gradien is -7 has coordinates:

First it says to find where the gradient is -7, so expand out the brackets (optional but can make it easier in this case) and find the derivative

To find the maximum interval where f(x) is strictly increasing or decreasing, why do we include the value of x where a stationary/s point is?

Because that's the definition of strictly increasing/decreasing. Although it may not technically be increasing/decreasing, we include it for strictly increasing/decreasing (but we wouldn't if it wasn't strictly). It's basically where the gradient doesn't change sign (so gradient can =0)

[ImmaculateJeff]

Hi!
Does anyone know of any good methods tutors that give really good notes + guidance + practice sheets? Im in dire need of a tutor so if please me some!
Thanks!