maximisation (1 Viewer)

[Kabeio]

Im a bit stuck on this maximisation question

An open tank, in shape of square prism, has square ends of side x cm and length l cm,

i) length, breadth and height have a sum of 15cm. Find an expression for the length l in terms of x

ii) show volume of tank is x²(15-2x)

iii) find maximum volume

PLease help, thanks!!

 

[Xayma]

i) Dimensions x*x*l

x+x+l=15cm
2x+l=15cm
l=15-2x cm

ii)V=x²l
=x²(15-2x)

iii) Find stat point of the above, prove it is maximum then sub the x value into V=x²(15-2x) to find volume

 

[FinalFantasy]

i) length, breadth and height have a sum of 15cm. Find an expression for the length l in terms of x
2x+l=15
l=15-x2
ii) show volume of tank is x²(15-2x)
V=area times height, so x² times ur l
therefore V=x²(15-2x)
iii) find maximum volume
V'=2x(15-2x)+-2(x²)=30x-6x²
V''=30-12x
put V'=0, so 30x-6x²=0
6x(5-x)=0
therefore x=0 or 5
x=5 will get u da maximum cuz when x=5 V''<0
So maximum volume=25(15-2(5))
EDITED: made differentiation error=P but ans. still right