Linear and Quadratic Approximations In Exercises 8588, use a graphing utility to graph

Chapter 4, Problem 85

(choose chapter or problem)

Linear and Quadratic Approximations In Exercises 85-88, use a graphing utility to graph the function. Then graph the linear and quadratic approximations

\(P_{1}(x)=f(a)+f^{\prime}(a)(x-a)\)

and

\(P_{2}(x)=f(a)+f^{\prime}(a)(x-a)+\frac{1}{2} f^{\prime \prime}(a)(x-a)^{2}\)

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)                                               \(a=\frac{\pi}{4}\)

Text Transcription:

P_1(x)=f(a) + f’(a)(x-a)

P_2(x)=f(a) + f’(a)(x-a)+1/2 f’’(a)(x-a)^2

P_1

P_2

a=pi/4