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It is an optimization problem
maybe some constraint given for height??
but how u know it is 10 sqrt （2） the question itself didnt give any restriction
so there are no constraints??
oh it actually says The machinery available cant fabricate material smaller than 2 cm in length but it doesnt really affect that 10sqrt (2)
The volume of a square-based rectangular cardboard box is to be 1000 cm3. Find the dimensions so that the quantity of material used to manufacture all 6 faces is a minumum. Assume that there will be no waste material. The machinery avaiable cannot fabricate material smaller in lenght than 2 cm.
or what is the domain in this question? for x
mathematically should be greater than zero ... or less than zero (technically discarded)
yea, but since the question says mustbe more than 2 so the domain is only x > 2?
cuz i think the domain is only for surface area but not volume
maybe the question is asking you to find the absolute maximum ...
yes it is but the teacher tells us to findthe domain too
the domain is value of x .. surface area and volume are range
what do u mean? i thought they are the same...
your given function is A(x) the value of A(x) is the range, and x is the domain
http://www.wolframalpha.com/input/?i=y+%3D+2x%5E2%2B4000%2Fx mathematically x can have any value excluding 0, that is your domain
ohhh but i have other questions that the domain has 2 restrictions .. let me see if i can figure it out first but thanks! i mixed up domain and range!!
here your domain is [0. 10sqrt(2)] ... i think it should be (0. 10sqrt(2)] since function is discontinuous at 0 adding another constraint that machine cannot make x less than 2, the new domain must be [2. 10sqrt(2)]
but i dont know where that 10sqrt(2) is from.. cuz that one is juz thetextbook answer
And u know for A = 1000x - 2x^2 i checked on that website, it shows domain is xer but actually the restriction is 0< x< 500
not .. the question has given you the domain
which ques u talking abt?
for this function A = 1000x - 2x^2, the domain is whole set of real number, but you can specify domain while defining function
OHHHH yes I get x can be any numbers but the question itself has restriction but the first question only tells u minimum is 2 so i guess the domain there will juz be x> 2
yes ...! some function are defined that way ... with a restriction.
Thanks ! srry for taking so much of ur time :)
it's all right ... you can learn a let by teaching too