Question: Consider the cost function \(C\left( x \right)=\frac{3}{10}{{x}^{3}}-\frac{1}{4}{{x}^{2}}+500x+200\). Say we are currently producing 7 units and plan to increase to 7.5.

(a) Use the approximation formula to estimate how the cost will change

(b) Use the marginal cost to estimate the cost of the 8^th unit

(c) Compute the actual cost of the 8^th unit.