Expression 17: 48 equals 4 times "x" squared plus 12 times "x" times "h" left parenthesis, "x" , right parenthesis48=4·x2+12·x·hx
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idet højden er givet ved:
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Expression 19: "h" left parenthesis, "x" , right parenthesis equals StartFraction, 48 minus 4 "x" squared Over 12 "x" , EndFraction left brace, 0 less than "x" less than StartRoot, 12 , EndRoot , right bracehx=48−4x212x0<x<12
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Expression 20: StartFraction, 12 minus "x" squared Over 3 "x" , EndFraction left brace, 0 less than "x" less than StartRoot, 12 , EndRoot , right brace12−x23x0<x<12
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Rumfanget R ( x ) bestemmes:
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Expression 22: "x" squared times StartFraction, 12 minus "x" squared Over 3 "x" , EndFraction left brace, 0 less than "x" less than StartRoot, 12 , EndRoot , right bracex2·12−x23x0<x<12
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Expression 23: StartFraction, 12 "x" squared minus "x" to the 4th power Over 3 "x" , EndFraction left brace, 0 less than "x" less than StartRoot, 12 , EndRoot , right brace12x2−x43x0<x<12
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Expression 24: StartFraction, 12 "x" minus "x" cubed Over 3 , EndFraction left brace, 0 less than "x" less than StartRoot, 12 , EndRoot , right brace12x−x330<x<12
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Expression 25: "R" left parenthesis, "x" , right parenthesis equals 4 "x" minus 1 third "x" cubed left brace, 0 less than "x" less than StartRoot, 12 , EndRoot , right braceRx=4x−13x30<x<12
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Expression 26: "R" prime left parenthesis, "x" , right parenthesisR′x
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Expression 27: StartFraction, "d" Over "d" "x" , EndFraction "R" left parenthesis, "x" , right parenthesisddxRx
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Expression 28: 4 minus "x" squared left brace, 0 less than "x" , right brace4−x20<x
Expression 32: "x" equals "x" Subscript, 1 , Baseline left brace, 0 less than "y" less than "R" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis , right bracex=x10<y<Rx1
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Størst muligt rumfang
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Størst muligt rumfang for 48 kroner: 5.3333333 cm ³