Answer
The change in annual cost when $Q$ is increased from $350$ to $351$ is equal to
$\dfrac{-668.7}{351}\approx-1.905$.
The instantaneous rate of change is more negative than the change in annual cost when $Q$ is increased from $350$ to $351$.
Work Step by Step
Substitute $Q=350$ in $C =\dfrac{1,008,000}{Q}+6.3Q$ and solve for $C$.
$C =\dfrac{1,008,000}{350}+6.3\times350=5085$
Now substitute $Q=351$ in $C =\dfrac{1,008,000}{Q}+6.3Q$ and solve for $C$.
$C =\dfrac{1,008,000}{351}+6.3\times351=\dfrac{1784166.3}{351}$
Now subtract the two costs to find the change in annual cost.
That is, $\dfrac{1784166.3}{351}-5085=\dfrac{-668.7}{351}\approx-1.905$
To find the instantaneous rate of change of annual cost at $Q=350$.
Firstly differentiate $C =\dfrac{1,008,000}{Q}+6.3Q$ with respect to $Q$.
We get, $C'=-\dfrac{1,008,000}{Q^2}+6.3$
Now substitute $Q=350$.
We get, $C'=-\dfrac{1,008,000}{350^2}+6.3=\dfrac{-2880}{350}+6.3=\dfrac{-675}{350}\approx-1.928$
The instantaneous rate of change is more negative than the change in annual cost when $Q$ is increased from $350$ to $351$.
