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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

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

Thanks

- hill
**Posts:**0**Joined:**Tue Mar 19, 2013 8:49 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!!

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
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 pm

Thanks Elisabeth!!

- hill
**Posts:**0**Joined:**Tue Mar 19, 2013 8:49 pm

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