Need help with a calculus question (1 Viewer)

[decimari]

Can someone help me with q. b) here http://imgur.com/wOCOQFF
Steps appreciated, thanks!

 

[Drsoccerball]

Can someone help me with q. b) here http://imgur.com/wOCOQFF
Steps appreciated, thanks!

Just use quotient rule ?

 

[DatAtarLyfe]

You use the perimeter formula for a sector (theta/360 *2*pi*r) and you make it equal to 18m (its given to you the perimeter is 18m)
Solve for r (if you look at the answer they want you to get, there is no r, only theta, so make r the subject)
Once you found r, use the area formula for a sector (theta/360*pi*r^2) and replace r with whatever you found above. Clean it up and you should get the answer.
For part b, differentiate you answer from part a to find max stationary point in terms of theta then sub it in to the area you found to find the max area

Edit: soz didn't see you needed help only with part b. Just use either quotient rule, or you can change the denominator to negative indices in order to use product rule

 

[decimari]

I ended using the product rule and I got theta = -1. I tested it with the first derivative test and it came up as a minimum point :| Where did I go wrong, aha.

 

[DatAtarLyfe]

Check you differentiation steps carefully, especially with the negative indices. If you know the quotient rule, try that instead of the product.
I got a positive answer, so if your still struggling i can give you the full working out

 

[davidgoes4wce]

This is my worked out solution

 

[InteGrand]

This is my worked out solution

 

[davidgoes4wce]

^^^ Yes your right, at theta =-2 it would be an undefined function. I should have stated that.

 

[InteGrand]

^^^ Yes your right, at theta =-2 it would be an undefined function. I should have stated that.