Chapter 12 - Sequences and Series - 12.3 Taylor Polynomials at 0 - 12.3 Exercises - Page 632: 41

4.6

The profit when x thousand tons of apples are sold is $P(x)=\ln(100+3x)$ $P'(x)=\frac{3}{100+3x}$ $P''(x)=\frac{-9}{(100+3x)^{2}}$ $P(0)=4.605$ $P'(0)=\frac{3}{100}$ $P''(0)=\frac{-9}{10000}$ $P_2(x)=4.605+\frac{3}{100}+\frac{\frac{-9}{10000}}{2!}x^{2}$ $P_{2}(x)=\frac{927}{200}-\frac{9}{20000}x^{2}$ $P_{2}(0.6)=\frac{927}{200}-\frac{9}{20000}(0.6)^{2} \approx 4.6$