A fish tank in the shape of a cuboid is to be made from 1600 cm of glass. The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin. (a) Show that the volume, V cm³, of the fish tank is given by V=400x (b) Given that x can vary, use differentiation to find the maximum or minimum value of V. (c) Justify that the value of V you found in part b is a maximum.

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Author:Bruce Crauder, Benny Evans, Alan Noell
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11. A fish tank in the shape of a cuboid is to be made from 1600 cmf of glass.
The fish tank will have a square base of side length x cm, and no lid. No glass is wasted.
The glass can be assumed to be very thin.
(a) Show that the volume, V cm³, of the fish tank is given by
V=400x*
(b) Given that x can vary, use differentiation to find the maximum or minimum value of V.
(c) Justify that the value of V you found in part b is a maximum.
Transcribed Image Text:11. A fish tank in the shape of a cuboid is to be made from 1600 cmf of glass. The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin. (a) Show that the volume, V cm³, of the fish tank is given by V=400x* (b) Given that x can vary, use differentiation to find the maximum or minimum value of V. (c) Justify that the value of V you found in part b is a maximum.
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