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Final Tips for 4U + some questions

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3.14159265359:
this is probably really dumb because its only 1 mark but this is what I did

dy/dx= ay(1-y)

max value when dy/dx=0

dy/dx=ay(1-y)=0
y=o or y=1

so where the freak does 1/2 come in the story?????

RuiAce:

--- Quote from: 3.14159265359 on October 22, 2018, 09:49:28 pm ---this is probably really dumb because its only 1 mark but this is what I did

dy/dx= ay(1-y)

max value when dy/dx=0

dy/dx=ay(1-y)=0
y=o or y=1

so where the freak does 1/2 come in the story?????

--- End quote ---
You're maximising the wrong thing. You've set \(\frac{dy}{dx} = 0\), but that maximises \( \boxed{y}\).

We actually want to maximise \( \boxed{\frac{dy}{dx}} \) itself. In theory, we would set \( \frac{d^2y}{dx^2} = 0\) to do this. But because we can't compute the corresponding second derivative, we just use our knowledge of quadratics to maximise it instead.

3.14159265359:

--- Quote from: RuiAce on October 22, 2018, 09:52:33 pm ---You're maximising the wrong thing. You've set \(\frac{dy}{dx} = 0\), but that maximises \( \boxed{y}\).

We actually want to maximise \( \boxed{\frac{dy}{dx}} \) itself. In theory, we would set \( \frac{d^2y}{dx^2} = 0\) to do this. But because we can't compute the corresponding second derivative, we just use our knowledge of quadratics to maximise it instead.

--- End quote ---

ohhhhhhhhhhhh


--- Quote from: RuiAce on October 22, 2018, 09:52:33 pm --- we just use our knowledge of quadratics to maximise it instead.

--- End quote ---
wdym?? and how?

I'm sorry I know this is dumb because its only 1mark

RuiAce:

--- Quote from: 3.14159265359 on October 22, 2018, 10:03:15 pm ---ohhhhhhhhhhhh
wdym?? and how?

I'm sorry I know this is dumb because its only 1mark

--- End quote ---
The maximum of a quadratic that concaves down occurs at its axis of symmetry, which is halfway between the intercepts (in this case at \(y=0\) and \(y=1\)).

3.14159265359:

--- Quote from: RuiAce on October 22, 2018, 10:11:03 pm ---The maximum of a quadratic that concaves down occurs at its axis of symmetry, which is halfway between the intercepts (in this case at \(y=0\) and \(y=1\)).

--- End quote ---

ohhhhhhhhh that makes sense, thank you!!!

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