Given the following polynomial functions, determine the endbehavior, x and y intercepts, multiplicity of zeroes/x-intercept,maximum number of turning points, and graph the givenpolynomial function.1.) y = x* (x – 3)³ (x + 5)2.) f(x) = (x + 1)²(x – 2)(x + 5)3.) F(x) = -x– 6x² + 9x + 14%3D

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Answered: Given the following polynomial…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The velocity of a faster asteroid is given as a function of time in this table: Time (second) Velocity (ms-1)t(0) = 10 250t(1) = 15 375t(2) = 20 525the velocity equation is v(t) = a0 + a1t + a2t2 Find out the velocity at tx = 17th second using second order polynomial interpolation
Give the degree and leading coefficient of the following polynomial function. Aa²) .2 f (x) = x³ (3 – 7æ² – 4æ²' - Degree: Number Leading Coefficient: Number
3. Sketch a rough graph of the following polynomial function, after describing the key characteristics of the function. f) = -2x(4 – 2x*)(x? - 1)? Degree Leading Coefficient (value) End Behaviour x -intercepts (including order) y-intercept What finite difference from the table of values of this function will be same and what will be its value?
12. For the polynomial p(x)=x²-2x²-x+2, determine the following then sketch the graph: a. Degree b. Roots including multiplicity End behavior C. d. y-intercept
18. For the following polynomial function, find: f(x)= (x-9)(x-6(x-3(x\x+3)(x+6)(x+9) The maximum number of peaks and valleys (local maxima and local minima) The maximum number of real zeros for the function 7.
2. Complete steps #A-E below and graph this polynomial: f(x) = x' + 3x² – 9x – 27 A) Find the zeros. (Show work.) B) Identify the multiplicity of each zero above. C) Divide the x-axis and use test values of x to determine signs. Interval Test Value Function Value f(x) Sign of f(x) D) Find f(0) = E) Use all of the information above to create an accurate sketch of this function. Draw it in the space to the right. ->

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Given the following polynomial functions, determine the end pehavior, x and y intercepts, multiplicity of zeroes/x-intercept, maximum number of turning points, and graph the given oolynomial function. 1.) y = x*(x – 3)³ (x+5) 2.) f(x) = (x + 1)²(x – 2)(x + 5) 3.) F(x) = -x³ – 6x? + 9x + 14