An orange is divided into 6 equal wedges. Jody eats 1 wedge. Then she eats 3 more wedges. How much of the orange did Jody eat?
2 answers:
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Answer:
Step-by-step explanation:
Volume =
find partial derivatives using product rule
i.e.
Using maximum for partial derivatives, we equate first partial derivative to 0.
y=0 or x+y =6
x=0 or x+4y =12
Simplify to get y =2, x = 4
thus critical points are (4,2) (6,0) (0,3)
Of these D the II derivative test gives
D<0 only for (4,2)
Hence maximum volume is when x=4, y=2, z= 4/3
Max volume is = 4(2)(4/3) = 32/3
Integrating gives
To compute the integral, substitute , so that
. Then
Since for all
, we can drop the absolute value, so we end up with
Given that , we have
so that
