Optimization of a Quadratic: 3-sides of a rectangular fence

[@nicholasreidpath862]

Clearest rectangle example I could find online

[@MrBdubsSAS]

Glad you liked it!

[@markle7428]

we can actually differentiate the function of the area to find the x value that will maximize the area enclosed.

[@briarrose9948]

Thank you so much! I have a math test next week, and this is very helpful:)

[@MrBdubsSAS]

Glad I could be of service!

[@andrewhowell7553]

Very nice, clear explanation. Well done

[@MrBdubsSAS]

The minimum area is 0. Since the range of this function can not go below 0, the lowest value it could be would be 0. If All of the fencing is used in a straight line, such that y = 1000m, the area would be 0. If it were a different question, with a different set of equations and different restrictions, such that the leading coefficient (the number in front of the x^2) was positive, there would be an absolute minimum, which you could find in exactly the same way, by finding the vertex.

[@ianrobb533]

Very helpful. Thank you

[@SuCKeRPunCH187]

how can you find the minimum area?