73–78 - Families of Polynomials Graph the family of polyno-mials in the same viewing rectangle, using the given values of c.Explain how changing the value of c affects the graph.73. P(x) = cx'; c = 1,2, 5, !74. P(x) = (x – c)*: c = -1,0, 1, 275. P(x) = x* + c; c = -1,0, 1, 2

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College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 19PS

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DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
4. Consider the function f(x) = √x. (a) Find the first and second Taylor polynomials for f at x = 1 . Use a graphing utility to compare these polynomials with f near x = 1. (b) Use these two polynomials to estimate √ 3 .
1. Using the given information about a polynomial function f(x), write its complete factored form: Degree: 4 Zero's (3,0) (2,0) (-1,0) Leading Coefficient: 1/2 2. Graph the derived function Thanks!
4.1 POLYNOMIAL FUNCTIONS: Determine the leading term (lt) the leading coefficient (lc), the degree of the polynomial (d) and the classification (c) Reference Example f(x) = – x + 3 + 4x2 f(x) = 4x3 + 2x2 +4x3 + x – 5 f(x) =– 1.1x3 - x4 + 0.3 x2 – 2.8x – 1.7
th degree polynomial function with rea n=3;3 and i are zeros; f(2)=25
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1 POLYNOMIAL FUNCTIONS: Determine the leading term (lt) the leading coefficient (lc), the degree of the polynomial (d) and the classification (c) Reference Example: f(x) =– x2 + 4x + 2 - 5x3 f(x) = 3 + 3x4 – 2x3 f(x) = -x6 + 2x2 – 5x - 6
3). Find the Taylor polynomial of degree two approximating the given function centered at the given point. f(x) = x at a = 4 p2(x) = please show step by step clearly .
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Dynamic profit function is P(t)= 2 - (t - 5) x ln (t + 1), here t is measured in years, and P is measured in hundreds of euros. a) use marginal analysis to estimate how fast company's profit was growing initially b) use Taylor formula to write down square approximation of the given profit function around t=2. Round coefficient of the Taylor polynomial to 3 decimals c) use results from step b) to estimate total company's profits between first and fourth years of operation d) estimate average company's profit between first and fourth years of operation e) use initial function to estimate total company's profits between first and fourth years of operation. Compare results with step c) the question is not graded, as the exam was yesterday, I want to check my answers
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73–78 - Families of Polynomials Graph the family of polyno- mials in the same viewing rectangle, using the given values of c. Explain how changing the value of c affects the graph. 73. P(x) = cx'; c = 1,2, 5, ! 74. P(x) = (x – c)*: c = -1,0, 1, 2 75. P(x) = x* + c; c = -1,0, 1, 2

73–78 - Families of Polynomials Graph the family of polyno- mials in the same viewing rectangle, using the given values of c. Explain how changing the value of c affects the graph. 73. P(x) = cx'; c = 1,2, 5, ! 74. P(x) = (x – c): c = -1,0, 1, 2 75. P(x) = x + c; c = -1,0, 1, 2