Chapter 2 - Derivatives - 2.7 Rates of Change in the Natural and Social Sciences - 2.7 Exercises - Page 180: 30

(a) $C(q)$ = $84+0.16q-0.0006q^{2}+0.000003q^{3}$ $C'(q)$ = $0.16-0.0012q+0.000009q^{2}$ $C'(100)$ = $0.16-0.0012(100)+0.000009(100)^{2}$ = $0.13$ (b) $C(101)-C(100)$ $\approx$ $97.13-97$ $\approx$ $0.13$ This is close to the marginal cost from part (a)

(a) $C(q)$ = $84+0.16q-0.0006q^{2}+0.000003q^{3}$ $C'(q)$ = $0.16-0.0012q+0.000009q^{2}$ $C'(100)$ = $0.16-0.0012(100)+0.000009(100)^{2}$ = $0.13$ (b) $C(101)-C(100)$ $\approx$ $97.13-97$ $\approx$ $0.13$ This is close to the marginal cost from part (a)