Answer:
Change in annual cost is 1.63 (decreasing).
Instantaneous rate of change is 1.65 (decreasing).
Step-by-step explanation:
Given that,

The annual change in cost is given by,

Calculate the value of cost at Q = 347 and Q =348 by substituting the value in cost function.
Calculating value of C at Q=347,


Calculating value of C at Q=348,


Substituting the value,


Negative sign indicate that there is decrease in annual cost when Q is increased from 347 to 348
Therefore, change is annual cost is 1.63 (decreasing).
Instantaneous rate of change is given by the formula,

Rewriting,

Now calculate \dfrac{C\left(Q+h\right) by substituting the value Q+h in cost function,

Therefore,

By using distributive law,

Cancelling out common factors,

Now, LCD of
and
is
. So multiplying first term by
and second term by
Therefore,

Simplifying,




Factoring out h from numerator,

Cancelling out h,

Calculating the limit by plugging value h = 0,


Given that Q=347,


Negative sign indicate that there is decrease in instantaneous rate when Q is 347
Therefore, instantaneous rate of change at Q=347 is 1.65 (decreasing).