Chapter 12 - Sequences and Series - 12.3 Taylor Polynomials at 0 - 12.3 Exercises - Page 632: 44

5.85

The profit when x thousand tons of apples are sold is $A(x)=\frac{6x}{1+10x}$ $A'(x)=\frac{6}{(1+10x)^{2}}=\frac{6}{100x^{2}+20x+1}$ $A''(x)=\frac{-1200x-120}{(100x^{2}+20x+1)^{2}}$ $A(0)=0$ $A'(0)=6$ $A''(0)=-120$ $A_2(x)=0+6-\frac{120}{2!}x^{2}$ $P_{2}(x)=6-60x^{2}$ $A_{2}(0.05)=6-60(0.05)^{2}=\frac{117}{20}=5.85$