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Consider the following polynomial function f(x) = x4 + 5x – 2x2 - 30x - 24...
Let f(x) = 2x2 - 12x2 - 30x-2. a. Find all points on the graph of...
Let f(x) = 2x2 - 12x2 - 30x-2. a. Find all points on the graph of f(x) at which the tangent line is horizontal. b. Find all points on the graph of f(x) at which the tangent line has slope 42. a. The tangent line is horizontal at the point(s) ; (Type an ordered pair. Use a comma to separate answers as needed.) b. The slope of the tangent line is 42 at the points) (Type an ordered pair. Use...
For the polynomial function f(x) = −5x(x + 2)2(x − 1)3: For the polynomial function f(x)...
For the polynomial function f(x) = −5x(x + 2)2(x − 1)3:
For the polynomial function f(x) = -5x(x + 2)(x - 1)": 7. (4 points) The leading term when expanded is -5.2". Use this to describe the end be havior of f(x): as r → , f(x) → as I + -00, f(x) → 8. (4 points) Name the zeros of f(x) and each of their multiplicities. 9. (4 points) Come up with a rational function which has y =...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
Given the quadratic function f(x) = -2(x – 2)2 + 8, please find the following: (a)...
Given the quadratic function f(x) = -2(x – 2)2 + 8, please find the following: (a) The vertex of the graph (b) The y-intercept of the graph in ordered pair (x, y) format. (c) The x-intercept(s) of the graph in ordered pair (x, y) format. (d) The direction which the graph opens and why you think this is true. (e) The axis of symmetry of the graph. Please show your work
10 For the given equation and graph of the quadratic function, do each of the following....
10 For the given equation and graph of the quadratic function, do each of the following. Complete parts (a) through (e). f(x) = -2(x - 5y2 + 2 a. Give the domain and range. The domain is (Type your answer in interval notation.) The range is (Type your answer in interval notation.) M h -10-8-82 2 -4 -6 -B 10 b. Give the coordinates of the vertex. The vertex is (Type an ordered pair.) c. Give the equation of the...
Analyze the polynomial function f(x)=x2 + x2 - 20x. Complete parts (a) through (c). (a) Find...
Analyze the polynomial function f(x)=x2 + x2 - 20x. Complete parts (a) through (c). (a) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are - (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is - (Type an integer or a simplified fraction.) (b) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph...
Sketch the following polynomial function using the four-step process. f(x)=x(x +2)x-3) The left-hand behavior starts and...
Sketch the following polynomial function using the four-step process. f(x)=x(x +2)x-3) The left-hand behavior starts and the right-hand behavior ends Find the y-intercept The y-intercept is 0.0 The real zeros of the polynomial are x (Use a comma to separate answers as needed Type an exact answer, using radicals as needed.) The multiplicity of the zero located farthest left on the x-axis is The multiplicity of the zero located between the leftmost and rightmost zeros is The multiplicity of the...
(2 points) Find the maximum and minimum values of the function f(x, y) = 2x2 +...
(2 points) Find the maximum and minimum values of the function f(x, y) = 2x2 + 3y2 – 4x – 5 on the domain x2 + y2 < 100. The maximum value of f(x, y) is: List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). The minimum value of f(x,y) is: List points where the function...
For the polynomial below, 3 is a zero. g(x) = x3 + 3x2 – 5x -...
For the polynomial below, 3 is a zero. g(x) = x3 + 3x2 – 5x - 39 Express g (x) as a product of linear factors. 8(x) = 0 x 5 ? Find all other zeros of P(x) = x + x + 4x + 30, given that 1 – 3i is a zero. (If there is more than one zero, separate them with commas.) x 6 ? The figure below shows the graph of a rational function f. It...
For the polynomial function f(x)=x^4+8x^3+16x2 answer the following: A. Using the leading coefficient test , determine...
For the polynomial function f(x)=x^4+8x^3+16x2 answer the following: A. Using the leading coefficient test , determine the graphs end behaviour. B. Find the X-intercepts and at which x-intercept does the graph cross the x-axis? C. At which x intercepts does the graph touch the x axis and turn around? D. What is the y intercept? E Determine whether the graph has y axis symmetry, origin symmetry or neithr. F.If necessary, find a few additional points and graph the function. Use...
Let f(x) = 2x2 - 12x2 - 30x-2. a. Find all points on the graph of f(x) at which the tangent line is horizontal. b. Find all points on the graph of f(x) at which the tangent line has slope 42. a. The tangent line is horizontal at the point(s) ; (Type an ordered pair. Use a comma to separate answers as needed.) b. The slope of the tangent line is 42 at the points) (Type an ordered pair. Use...
For the polynomial function f(x) = −5x(x + 2)2(x − 1)3:
For the polynomial function f(x) = -5x(x + 2)(x - 1)": 7. (4 points) The leading term when expanded is -5.2". Use this to describe the end be havior of f(x): as r → , f(x) → as I + -00, f(x) → 8. (4 points) Name the zeros of f(x) and each of their multiplicities. 9. (4 points) Come up with a rational function which has y =...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
10 For the given equation and graph of the quadratic function, do each of the following. Complete parts (a) through (e). f(x) = -2(x - 5y2 + 2 a. Give the domain and range. The domain is (Type your answer in interval notation.) The range is (Type your answer in interval notation.) M h -10-8-82 2 -4 -6 -B 10 b. Give the coordinates of the vertex. The vertex is (Type an ordered pair.) c. Give the equation of the...
Analyze the polynomial function f(x)=x2 + x2 - 20x. Complete parts (a) through (c). (a) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are - (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is - (Type an integer or a simplified fraction.) (b) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph...
Sketch the following polynomial function using the four-step process. f(x)=x(x +2)x-3) The left-hand behavior starts and the right-hand behavior ends Find the y-intercept The y-intercept is 0.0 The real zeros of the polynomial are x (Use a comma to separate answers as needed Type an exact answer, using radicals as needed.) The multiplicity of the zero located farthest left on the x-axis is The multiplicity of the zero located between the leftmost and rightmost zeros is The multiplicity of the...
(2 points) Find the maximum and minimum values of the function f(x, y) = 2x2 + 3y2 – 4x – 5 on the domain x2 + y2 < 100. The maximum value of f(x, y) is: List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). The minimum value of f(x,y) is: List points where the function...
For the polynomial below, 3 is a zero. g(x) = x3 + 3x2 – 5x - 39 Express g (x) as a product of linear factors. 8(x) = 0 x 5 ? Find all other zeros of P(x) = x + x + 4x + 30, given that 1 – 3i is a zero. (If there is more than one zero, separate them with commas.) x 6 ? The figure below shows the graph of a rational function f. It...
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