Linear and Quadratic Approximations In Exercises 8184, use a graphing utility to graph
Chapter 4, Problem 82(choose chapter or problem)
Linear and Quadratic Approximations
In Exercises 81–84, 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 = 0
Equation Transcription:
Text Transcription:
P_1 (x) = f(a) + f ^prime (a)(x-a)
P_2 (x) = f(a) + f ^prime (a)(x-a) + 1/2 f^prime ^prime (a)(x-a)^2
f
P_1
P_2
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