12. Use the graph of the polynomial f(x) to answer the questions belowa. Is f(x) even, or odd, or neither? Why?b. Does it have any local extrema?If yes what is its value? If no, why not?c. Does it have any absolute extrema?If yes what is its value? If no, why not? d. Give the intervals where the function is increasing and decreasinge. What is the smallest possible degree of f(x)?

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Answered: Use the graph of the polynomial f(x) to…

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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1. If any of the linear factors of a polynomial function are squared, then which of the following is not true o corresponding x-intercepts? The x-intercepts are turning points of the curve. b. a. The x-axis is tangent to the curve at these points. The graph passes through the x-axis at these points. d. с. The graph has a parabolic shape near these x-intercepts. 2. Which graph is a possible sketch of the function g(x) = (x+ 1) (x- 2)? 30+ 30 + 24 + 24 + 18+ 18- 12+ 12- 6+ 6+ +%> 3 4 5 -54 -3 -2 -6+ 2 -5 -4 -3 3 4. -6+ -12- -12 + -18+ -18 + -24 + --24 + -30- -30+ a. с. 个) 30+ 30 24+ 24 - 18+ 18+ 12+ 12+ 6+ 6- ++ -5 -4 -3 -2 /-1 -6 I 2 3 4 5 x -5 4 -3 -2 -1 -6+ 2 3 4 5 x -12+ -12+ -18 + -18+ -24 - -24 + -30+ b. -30 + d. 3. Which equation is a quartic function with zeros at-4,-1, 2, 3? a. y = (x-4)(x – 1)(x+2)(x +3) b. y = (x-2)(x- 3)(x+4)(x+1) c. y = (x+4) (x + 1)(x – 2)°(x – 3) d. y= (x+4) (x + 1)°(x – 2)°(x – 3)²
For the following polynomial: f(x) = (x – 1)2 ( x2– x – 30) 3a) Describe the end behavior of the graph. (You 3b) Find the x and y-intercepts 3c) Is the graph of this function both smooth and continuous? Explain why or why not? 3d) Provide a sketch of the function. How did you use your answers to parts (a), (b), and (c) to sketch the graph.
p. 4 31. Consider the polynomial, f(x) = x +x Notice, toq, the function has a negative value when x 1, and yet it's positive when x 3. Therefore, you can conclude that f(x) must have a zero between x 1 - 5x - 6, and notice that f(1) =-9 and f(3) =15. కాంతంశశు 1 and x 3 because of what important theorem? (a) The Zero Factor Theorem (c) The Fundamental Theorem of Algebra (b) The Intermediate Value Theorem (d) The Remainder Theorem
Consider f (x) = 2x* – x3 – 5x2 + 2x + 2. 1. List all possible zeros (candidates) for f(x). 2. Define f (x) in your calculator or desmos. Use the graph to narrow down your candidates. Use synthetic division to reduce f (x) to a quadratic expression. Factor the resulting quadratic expression to find the last two zeros. ZEROS: 3. Express f(x) as a product of linear factors. Don't forget to include the value of a!

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Use the graph of the polynomial f(x) to answer the questions below a. Is f(x) even, or odd, or neither? Why? b. Does it have any local extrema? If yes what is its value? If no, why not? c. Does it have any absolute extrema? If yes what is its value? If no, why not?