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# C2 Problem (Differentiation) watch

1. I was doing question 9 in the Edexcel C2 specimen paper and it was all going well until they told me to differentiate this...

A=1/4(x^3-7x^2+8x+16) where A is the area of a triangle, and the question is asking to prove that A is a maximum when x=2/3

In the solution it says "ignore the 1/4", which ive done and it comes out fine, but I don’t understand why ive been able to ignore it. And also in the solutions when they prove that its a maximum they put the 1/4 back and say

D2A/DX2=1/4(6x-14), which is <O so is a maximum.

Which confused me more

I think I should go to bed now cos its 11.29

Thanks a lot

Rob
2. It's basically becauase you know you'll be setting dA/dx to zero.

So think of writing 4A = ...

Then 4dA/dx = ....

0 = ....

They're just putting the factor back afterwards to be a bit rigorous. Although we can see that it won't affect the answer in this case it might have been a negative factor for example, which would have meant disregarding it in the first part was still valid but putting it back in the second part is crucial.
3. (Original post by bertus)
I was doing question 9 in the Edexcel C2 specimen paper and it was all going well until they told me to differentiate this...

A=1/4(x^3-7x^2+8x+16) where A is the area of a triangle, and the question is asking to prove that A is a maximum when x=2/3

Rob
A = (4x^3-28x^2+32x+64)^-1
dA/dx = (-(4x^3-28x^2+32x+64)^-2) x (12x^2-56x+32)
(12x^2-56x+32)(-4x^3+28x^2-32x-64)^-2

Turning points at dA/dx = 0
(12x^2-56x+32)(-4x^3+28x^2-32x-64)^-2 = 0

In the above equation just substitute x = 2/3
If the equation gives 0, then you know that point A (x = 2/3) is a turning point, as you substitute you'll see that the first bracket gives 0, hence this equation is 0.

To prove the turning point to be a maximum, differentiate the derivative and see if d²A/dx² at point (x = 2/3) is +/-, if plus then minimum, if - then maximum.
It should be a negative number as you say its a maximum.

Hope that helps, if you need further help, just ask.

Vijay

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