Find the Taylor polynomial of degree 3 for the function f(x) = 2+about x = 3. T3(x) = +[ |(x − 3) + (x − 3)² + (x − 3)³

2. Find the formula for the fourth degree polynomial containing the point (0,8) and whose graph is given below. y-int-8 -1 3.

Here is some information about a function ƒ : f is a polynomial function of the form f (x) = Ax² + Bx + C. f'(x) = 4x – 3 The graph off contains the point (-1,7). Use this information to determine f(x). That is, find the values of A, B , and C.

Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and x = n1 + 1, and another integer n2 so that f(x) has a root between x = n2 and x = n2 + 1.

steps. For the function h(x) = −2x³ - 4x + 3√x, calculate h'(x), h'' (x), and h''' (x) . Show all 2 h(x) = -6x² - 4+ 3 ī h"(x) = 4 (+6x²-4 + 3 = 2√x h(x) = -2x 3-4x +3√3 dx 2√x h "(x) = 2 ( 6x²)_ _d (4) + d( 2 dx dx h"(x) = -60 • 2x+0-3x21 2. h²(x)= x (-2x ³ - 4x + 3√x 2 3 n'(x) = d (-2x ³) + d (-4x) + d (3√x) dx dx h'(x) = (2) (3x²+4+3 (1) 2 |h²(x) = -6x ² - 4 + ²³ 3 25 2√√x √ 3|hx)=12x-3 4x-√7 hly--12x n(x) = d (~3) • (4x√7) - d (4x√x) = (-3) 4 = 4• zx : -12 dx 4XXX 4x -3 x 1 4x X2 4/2 Ex -6.1X (2 h" (x) = -67-3x • 2 (₁x) (2√x)2 h(x=-12x-3) -3 4x√x

4. Consider the polynomial f(x) = x² + 1. (a) Show that f (x) is irreducible in (Z/3Z) [x]. (b) Show that f(x) is reducible in (Z/2Z) [x], and factor it as a product of irreducibles.

pls help asap

1. The zeros of the polynomial function f (x)=x' – 2x² – 15x are: a. {-5,–3,0} . b. {-3,5} . c. {-5,3} . d. {-5,0,3} . e. {-3,0,5} .

3. Let f(x) be a polynomial function such that f(3) is 7, the first derivative,f(3) is 0, and the second derivative, f¨(3) is -2. The point (3, 7) is a of the graph of f.

Find the linear approximating polynomial for the function centered at a. 1 f(x) = x + - a = 3 - x' 8 1 O A. L(x)=D 및+ ** 2 2 8 B. L(x)=D 잊+ 10 1 OC. L(x) = -X + 2 10 2 D. L(x) = FX + - 3