minimum problem (1 Viewer)

[MrBrightside]

alright, good to be back.

have this slight issue I can't get over.

did part (a) correctly which is as follows:

View attachment 22441

part (b) I do not know how to get past the first derivative correctly.

stuck on A' = 4pir - 750r^-2 = 0

to find stationary points. thanks, any help is really appreciated.

 

[hscmathstutor10]

alright, good to be back.

have this slight issue I can't get over.

did part (a) correctly which is as follows:

View attachment 22441

part (b) I do not know how to get past the first derivative correctly.

stuck on A' = 4pir - 750r^-2 = 0

to find stationary points. thanks, any help is really appreciated.

This is very similar to the one I did on the hscguide site ( I assume you are "brightside11" on that site ) , have a look there for the soln

 

[hscmathstutor10]

so S= 2 pi r^2 + 750/r
S= 2 pi r^2 + 750r^-1
dS/dr = 4 pi r -750r^-2 = 4 pi r -750 / r^2 = 0 for min/max

so 4 pi r = 750 / r^2
4 pi r^3 = 750
r= ( 750 / (4pi) ) ^(1/3)


now d^2 S/dr^2 = 4 pi +1500r^-3 = 4pi +1500/r^3 which is positive for all positive r, so we have a concave down graph, and a minium value

 

[4025808]

alright, good to be back.

have this slight issue I can't get over.

did part (a) correctly which is as follows:

View attachment 22441

part (b) I do not know how to get past the first derivative correctly.

stuck on A' = 4pir - 750r^-2 = 0

to find stationary points. thanks, any help is really appreciated.

All you got to do is make r the subject. That is as shown below

4pir = 750/r^2
now
r^3= 750/4pi
r = (750/4pi)^(1/3)
r = approx 3.9
test this to make sure it is the minimum (markers want you to do this).

ask me if this doesn't help

 

[MrBrightside]

ahh yes...just before I posted this, I had forgot, I asked you about a similar qs... bahahah.
hscmaths thanks a lot man, really thankful. your working out was really easy to understand. I was stuck on the smallest part. Now I clearly understand it. thank you.

 

[MrBrightside]

smack bam! 3.9 cm so happy now, thanks guys.