For a small manufacturing company, the total cost C (in dollars) of producing q widgets is modeled for 0≤q≤600 by the differentiable function
C(q)=0.005q3−0.4q2+15q+2000,
where q is measured in widgets.
(a) Calculate C′(q) and state the units of C′(q).
(b) Evaluate C′(300) and interpret the meaning of this value in the company’s context.
(c) Using your answer to part (b), estimate the additional cost of increasing production from 300 to 301 widgets. Justify your estimate verbally.