Over the first two years, at what time t is the amount of honey in the hive the most? What is this maximum value? Explain and justify your answers fully 1. As a hive of bees makes and uses its honey, the bees are adding honey at a rate describedby the functionTth(t) = 4 sin)+ 1.Meanwhile, a bee keeper starts taking honey from the hive as a rate modeled by thefunction3tk(t) =10+ 3tBoth h(t) and k(t) are measured in kilograms per month, t is measured in months andthe valid times are 0

Answered: Over the first two years, at what time…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Over the first two years, at what time t is the amount of honey in the hive the most? What is this maximum value? Explain and justify your answers fully

1. As a hive of bees makes and uses its honey, the bees are adding honey at a rate described
by the function
Tt
h(t) = 4 sin
)
+ 1.
Meanwhile, a bee keeper starts taking honey from the hive as a rate modeled by the
function
3t
k(t) =
10+ 3t
Both h(t) and k(t) are measured in kilograms per month, t is measured in months and
the valid times are 0 <t < 24. At time t=0, there are 10 kg of honey in the hive.

Expert Solution

Step 1

Maxima and minima of a real-valued function is a very important application of differentiation. At the critical point, there is no rate of change of the function. After the stationary point, if the function increases, at the stationary point, the function becomes minimum. If the function increases before the critical point and decreases after the critical point, the function gets the maximum value at this point. A function can have more than one critical point. The first-order and second-order derivative tests are used to evaluate the extremum of a function.