In Exercises 95 and 96, use a graphing utility to graph the function. Then graph and in

Chapter 5, Problem 96

(choose chapter or problem)

Linear and Quadratic Approximations In Exercises 95 and 96, use a graphing utility to graph the function. Then graph

\(P_{1}(x)=f(0)+f^{\prime}(0)(x-0)\)      and

\(P_{2}(x)=f(0)+f^{\prime}(0)(x-0)+\frac{1}{2} f^{\prime \prime}(0)(x-0)^{2}\)

in the same viewing window. Compare the values of f, \(P_{1}\), and \(P_{2}\) and their first derivatives at x = 0.

\(f(x)=e^{x / 2}\)

Text Transcription:

P_1 (x) = f(0) + f’(0)(x - 0)

P_2 (x) = f(0) + f’(0)(x - 0) + 1/2 f’’(0)(x - 0)^2

P_1

P_2

f(x) = e^x/2