Help appreciated (1 Viewer)

[mattstonestreet]

Just going throught the '97 maths paper and em having difficulty with 6iii. If you do the question you can see that this is part of the simplification after differentiation. So basically I need to simplify this. If you write it out it isn't as bad as it looks here!

1/2(25-10x)^1/2 + 1/2x((2(25-10x)^1/2)^-1 =0

 

[Riviet]

Let A=1/2.x(25-10x)^1/2

dA/dx=1/2.{sqrt(25-10x) - 5x/sqrt(25-10x)} by product and chain rule

When dA/dx=0,

1/2.{sqrt(25-10x) - 5x/sqrt(25-10x)}=0

sqrt(25-10x) = 5x/sqrt(25-10x)

[sqrt(25-10x)][sqrt(25-10x)]=5x

25-10x=5x

15x=25

x=5/3

Then substitute this into A to find maximum area. You should also show that it's a max at this x value either using first or second derivative. Hope that helps.

 

[Aaron06]

^^ Beat me too it. =[

 

[mattstonestreet]

Thanks! That really helped