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Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(–h + 10)(–h + 8). What is the maximum volume for the domain 0 < h < 10? Round to the nearest cubic foot.

 

10 ft^3

 

107 ft^3

 

105 ft^3

 

110 ft^3

 Jan 29, 2019
 #1
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 V(h) = h(–h + 10)(–h + 8)  =  h ( h^2 - 18h + 80)  = h*3 - 18h^2 + 80h

 

Look at the graph here, LGB...

 

 

The max volume on the interval  occurs at (2.945, 105.028)

 

So...the max volume is about 105 ft^3

 

 

cool cool cool

 Jan 29, 2019

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