VCE Methods Question Thread!

[minhalgill]

does anyone know how to do this?

[GMT. -_-]

does anyone know how to do this?

Unless I'm mistaken, since A,B and D don't satisfy the given condition, we can immediately omit those options immediately.
If f(x) was e^x, then h'(x) would be f'(x)g(x)+f(x)g'(x) = e^x(g(x)+g'(x)) which does not equal f(x)g'(x) = e(x) g'(x).
If f(x) was 1, then h'(x) would also equal the same expression f'(x)g(x)+f(x)g'(x), which equals 0 g(x) + 1 g'(x) when you sub in the condition f(0) = 1 and by knowing the derivative of y =1 is 0.
Even without testing the case of f(x) being 1, by logic E is the answer.
Hope this helps!

[minhalgill]

For 13, how is p=0.8 and not 0.2?
thanks

[snip]

Since 20% of people have been unemployed, that means that 80% of people have not been unemployed, which is what the question is asking for.

[DinWell]

How do I prove that \[ \frac{4}{\sqrt[3]{4}+\sqrt[3]{2}+2}=4-\sqrt[3]{2^{5}} \]?

[fun_jirachi]

[passbleh24]

Hey,

In question 20 they use the relationship f'(x) x f'(y) = 1, where is this from and what does it actually mean?

And I'm really struggling to understand question 17 and am unable to see the relationship between the anti and dif function. The answer is E

Edit: I think I'm starting to see the relationship for question 17. f( x) is the derivative of F( x). Anti diffing f( x) would give F( x). F(8 ) - F(4 ) + F(4 ) = F(8 ). Still struggling with 20.

Thank you for any assistance

[S_R_K]

Hey,

In question 20 they use the relationship f'(x) x f'(y) = 1, where is this from and what does it actually mean?

This question was asked and answered earlier in the thread, see: https://atarnotes.com/forum/index.php?topic=128232.msg1074057#msg1074057

[Freddie Hg]

can someone please explain question 20 of the nht methods exam, i equated the deravitive to 0 and found x=(1-a)^1/2, i got this value and equated it less than or equal to two, as the last possible turning point has to be at 2. but i dont get the answer?? can anyone help?

so does anyone have a clue on this q??

[passbleh24]

This question was asked and answered earlier in the thread, see: https://atarnotes.com/forum/index.php?topic=128232.msg1074057#msg1074057

"Easiest way to do this one is to realise that if two lines are reflections of each other about the line y = x, then their gradients will be reciprocals of eachother."

Thank you I wasn't aware of this relationship makes sense now !!

[S_R_K]

so does anyone have a clue on this q??

The inverse exists for x ≥ 2 if and only if the function is strictly increasing (or strictly decreasing, but we can rule out this possibility quickly) for all x ≥ 2.

Hence, we need to find all values of a for which f'(x) is non-negative when x ≥ 2. So, we find the derivative, and then factorising gives us f'(x) = 4(x – 2)(x^2 + 2x + a). This will be non-negative for all x ≥ 2 if x^2 + 2x + a is non-negative when x ≥ 2. So, we let x = 2 and solve for a, and find that a = –8. Then, since x^2 + 2x + a > x^2 + 2x – 8, for all a > –8 (and when x ≥ 2), we conclude that a ≥ –8 gives us f'(x) is non-negative when x ≥ 2.

[Freddie Hg]

The inverse exists for x ≥ 2 if and only if the function is strictly increasing (or strictly decreasing, but we can rule out this possibility quickly) for all x ≥ 2.

understood your approach only the part where you ruled out it being strictly decreasing ^^

[S_R_K]

understood your approach only the part where you ruled out it being strictly decreasing ^^

Sorry, do you mean that the part where we can rule out the function being strictly decreasing is the only part you understood, or the only part you did not understand?

[Freddie Hg]

Sorry, do you mean that the part where we can rule out the function being strictly decreasing is the only part you understood, or the only part you did not understand?

the ruling out part, like i completely get maintaining the function to stay strictly increasing, but why cant it be strictly decreasing to? it would still remain a one to one function??

[DinWell]

Wow, thanks. Would never have thought of that. This came up on a neap exam where I did it differently to the paper. I was wondering if 2 answers like this was possible in an exam question, would they both be accepted even if one is much more complicated?