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a box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides. what is the maximum volume this box could have? (round your answer to two decimal places.)



Answer :

Maximum volume through the concept of maxima is 564.22 cm3.

What are maxima?

  • The maxima are discovered using the arithmetic of variations if the domain of the function for which the maxima is sought consists solely of functions (i.e., if the maxima sought of a functional).
  • There are no any minimum or maximum values in unlimited infinite collections, for example the collection of real numbers.

Volume of box=(50-2x)(10-2x).x

=4x^3-120x^2+500x

for maximum volume,

dv/dx=0

⇒12x^2-240x+500=0

⇒3x^2-60+14=0

x=17.63,2.36

d2v/dx2=24x-240

at x=2.36

d2v/dx2<0

∴x=2.36

v will be maximum

Maximum volume through the concept of maxima is 564.22 cm3.

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