Answer
$\dfrac{dS}{dQ}=-2882Q^{-2}-0.052$
$\dfrac{d^{2}S}{dQ^{2}}=5764Q^{-3}$
Work Step by Step
Given formula is $S = 2882Q^{−1} − 0.052Q + 31.73$.
Use the power rule to find the first derivative.
$\dfrac{dS}{dQ}=-2882Q^{-2}-0.052$
Now again use the power rule to find the second derivative.
$\dfrac{d^{2}S}{dQ^{2}}=-2882\times(-2)Q^{-3}=5764Q^{-3}$
