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Answer:
The value of double derivative at x=4.834 is negative, therefore the trough have a maximum volume at x=4.834 inches.
Step-by-step explanation:
The dimensions of given metal strip are
Length = 160 inch
Width = 20 inch
Let the side bend x inch from each sides to make a open box.
Dimensions of the box are
Length = 160-2x inch
Breadth = 20-2x inch
Height = x inch
The volume of a cuboid is
Volume of box is
Differentiate with respect to x.
Equate V'(x)=0, to find the critical points.
Using quadratic formula,
The critical values are
Differentiate V'(x) with respect to x.
The value of double derivative at critical points are
Since the value of double derivative at x=4.834 is negative, therefore the trough have a maximum volume at x=4.834 inches.