Approximating functions by Taylor Polynomials.

Chapter 4: Taylor Series 17 same derivative at that point a and also the same second derivative there. We do both at once and deﬁne the second degree Taylor Polynomial for f (x) near the point x = a. f (x) ≈ P 2(x) = f (a)+ f (a)(x −a)+ f (a) 2 (x −a)2 Check that P 2(x) has the same ﬁrst and second derivative that f (x) does at the point x = a. 4.3 Higher Order Taylor Polynomials

Taylor