Textbook Problem

Linear and Quadratic Approximations In Exercises83-86, use a graphing utility to graph the function. Then graph the linear and quadratic approximations

$P_1(x)=f(a)+f^{\text{'}}(a)(x-a)$

and

$P_2(x)=f(a)+f^{\text{'}}(a)(x-a)+\frac{1}{2}{f}^n(a){(x-a)}^2$

in the same viewing window. Compare the values of f, $P_1$, and $P_2$, and their first derivatives at $x=a$ . How do the approximations change as you move farther away from $x=a?$

Function Value of a

$f(x)=2(\sin x+\cos x)$ $a=0$