IB Math Studies Optimization problems

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IB Math Studies Optimization problems

Postby hill » Mon Apr 15, 2013 7:25 pm

IB Mathematical Studies SL – Calculus, Derivatives, Differentiation, Optimization problems


How can we find the largest area of a rectangular region having perimeter 600 m ?


Thanks
hill
 
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Re: IB Math Studies Optimization problems

Postby elizabeth » Mon Apr 15, 2013 7:37 pm

IB Mathematical Studies SL – Calculus, Derivatives, Differentiation, Optimization problems

Let be the dimensions of the rectangular region and be its area. We want to find the largest value of A.
We know that . We need to eliminate using the fact that

Thus the function described the area can be written as


Therefore the problem now is to maximize the function
To find the maximum of , we find the stationary points



Since

the function is increasing for

and



the function is decreasing for


So, the function has a maximum when

and the largest area of a rectangular region is



Therefore the rectangular is a square


Hope these help!!
elizabeth
 
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Re: IB Math Studies Optimization problems

Postby hill » Mon Apr 15, 2013 7:43 pm

Thanks Elisabeth!!
hill
 
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