A rectangular area adjacent to a river is to be fenced in, butno fencing is required on the side by the river. The total area tobe enclosed is 114,996 square feet. Fencing for the side parallelto the river is $6 per linear foot, and fencing for the other twosides is $7 per linear foot. The four corner posts cost $25 apiece.Let xx be the length of the one the sides perpendicular to theriver.

[A] Find a cost equation C(x)C(x):
C(x)=C(x)=    

[B] Find C'(x)C?(x):
C'(x)=C?(x)=    

[C] Find the appropriate critical value(s) for theappropriate domain in the context of the problem.
   

[D] Perform the second derivative test todetermine if there is an absoulte minimum at the critical valuefound.
C''(x)=C??(x)=   

[E] What is the best conclusion regarding anabsolute maximum or minimum at this criticalvalue. (MULTIPLE CHOICE)

a) At the critical value C''(x)>0C??(x)>0 so I canconclude that there is a local/relative maximum there but I can'tconculde anything about an absolute maximum for x>0x>0

b) Since C''(x)>0C??(x)>0 for all x>0x>0 we cancolude that the CC is concave up for all values of x>0x>0 andthat we therefore have an absolute minimum at the critical valuefor x>0x>0

c) Since C''(x)>0C??(x)>0 for all x>0x>0 we cancolude that the CC is concave up for all values of x>0x>0 andthat we therefore have an absolute maximum at the critical valuefor x>0x>0

d) The second derivative test is inclusive with regards to anabsolute maximum or minimum and the first derivative test should beperformed

e) At the critical value C''(x)>0C??(x)>0 so I canconclude that there is a local/relative minimum there but I can'tconculde anything about an absolute minimum for x>0x>0

[F] Find the minimum cost to build the enclosure:$

*Please show all work associated*