Chapter 12 - Sequences and Series - 12.3 Taylor Polynomials at 0 - 12.3 Exercises - Page 632: 43

570.5

The profit when x thousand tons of apples are sold is $R(x)=500\ln(4+\frac{x}{50})$ $R'(x)=\frac{500}{200+x}$ $R''(x)=\frac{-500}{(200+x)^{2}}$ $R(0)=693$ $R'(0)=\frac{5}{2}$ $R''(0)=\frac{-5}{2}$ $R_2(x)=693+\frac{5}{2}-\frac{\frac{5}{2}}{2!}x^{2}$ $P_{2}(x)=\frac{1391}{2}-\frac{5}{4}x^{2}$ $P_{2}(10)=\frac{1391}{2}-\frac{5}{4}10^{2}=\frac{1141}{2}=570.5$