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2006 Paper 2 Question 12 b - HSN forum

# 2006 Paper 2 Question 12 b

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### #1Philip

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Posted 20 May 2009 - 10:43 AM

Need some help with the 2006 Paper 2 Question 12 b

Thanks!
Yeah!

### #2Garden

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Posted 20 May 2009 - 11:24 AM

QUOTE (Philip @ May 20 2009, 11:43 AM) <{POST_SNAPBACK}>
Need some help with the 2006 Paper 2 Question 12 b

Thanks!

Handily you can find the HSN worked solution at Google Books but here's how I would do it (not too different really)...

Remember that extremes (that is the mins and maxes) can occur at stationary points or the start and end of the given range (underlined as that's probably what you've done wrong )

So, A = 80 - 12x - 48^-1
dA/dx = -12 + 48x^-2 = 0 (for stat. point)
-12 + 48/x^2 = 0
48/x^2 = 12
12x^2 = 48
x^2 = 4
x = 2 or -2
Thus x = 2 as x > 0.

So find A for the three values of x...
When x = 1, A = 80 - 12x1 - 48/1^2 = 20
When x = 2, A = 80 - 12x2 - 48/2^2 = 32
When x = 4, A = 80 - 12x4 - 48/4^2 = 20

Therefore: Max of A is 32 when x = 2 and Min of A is 20 when x = 1 or 4
Beware negatives,
for they will haunt you in haikus
and in exam rooms.

### #3Philip

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Posted 20 May 2009 - 01:26 PM

QUOTE (Garden @ May 20 2009, 12:24 PM) <{POST_SNAPBACK}>
QUOTE (Philip @ May 20 2009, 11:43 AM) <{POST_SNAPBACK}>
Need some help with the 2006 Paper 2 Question 12 b

Thanks!

Handily you can find the HSN worked solution at Google Books but here's how I would do it (not too different really)...

Remember that extremes (that is the mins and maxes) can occur at stationary points or the start and end of the given range (underlined as that's probably what you've done wrong )

So, A = 80 - 12x - 48^-1
dA/dx = -12 + 48x^-2 = 0 (for stat. point)
-12 + 48/x^2 = 0
48/x^2 = 12
12x^2 = 48
x^2 = 4
x = 2 or -2
Thus x = 2 as x > 0.

So find A for the three values of x...
When x = 1, A = 80 - 12x1 - 48/1^2 = 20
When x = 2, A = 80 - 12x2 - 48/2^2 = 32
When x = 4, A = 80 - 12x4 - 48/4^2 = 20

Therefore: Max of A is 32 when x = 2 and Min of A is 20 when x = 1 or 4

For the three values at the end: did you just use the x=1 and x=4 from the graph to find the mins and maxs?

What i did wrong was that i found the minimum x=2, but didn't know you just subbed in the other two values.

Thanks for the help

Yeah!

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