Chapter 4.3, Problem 61E

Business: increasing total cost. Kitchens-to-Please Contracting determine that the marginal cost, in dollars per square foot, of installing x square feet of kitchen countertop is given by

$C^{\prime }\left(x\right)=4x^{1/3}$.

a. Find the cost of installing $50{\text{ft}}^2$ of countertop

Find the cost of installing an extra $14{\text{ft}}^2$ of countertop after $50{\text{ft}}^2$ have already been installed.