We can resolve this issue by discovering a feature of the location in regards to x. For this, we observe the adhering to:
$ latex AB+BC= 6$
$ latex x+ BC= 6$
$ latex BC= 6-x$
Then, we can utilize the triangular location formula to obtain:
$ latex A= frac {1} {2} times BC times AB$
$ latex A= frac {1} {2} (6-x) x$
$ latex A= 3x-frac {x ^ 2} {2} $
Now, we need to discover the by-product to develop a formula as well as discover the fixed factors:
$ latex A( x)= 3x-frac {x ^ 2} {2} $
$ latex A'( x)= 3-x$
$ latex 3-x= 0$
$ latex x= 3$
We check whether this factor is an optimum factor utilizing the 2nd acquired:
$ latex A ^ {prime prime} (x)= -1$
Since $latex f ^ {prime prime} (x)
$ latex A= 3x-frac {x ^ 2} {2} $
$ latex A= 3( 3 )- frac {(3 )^ 2} {2} $
$ latex A= frac {9} {2} =4.5$
The optimum location of the triangular is 4.5 centimeters ².