x +bhas vertical asymptotes at x=-2 and x=2. Given f'(x)=* -aA function f (x)=%3DFind:i) The values of a and bii) The horizontal asymptote(s), critical point and inflection point(s), interval ofincreasing, decreasing, concave up and down, and finally sketch the graph.

The function f(x)=x2+bx2-a has vertical asymptotes x=-2 and x=2.f'(x)=-12x(x2-a)2

Answered: A function f(x) = x +b has vertical…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 15T

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The tangent line to the graph of f(x) at x = 2 is shown. On the tangent line, P is the point of tangency and A is another point on the line. The x y-coordinate plane is given. There is 1 curve and 1 line on the graph. The curve enters the window in the second quadrant, goes down and right becoming less steep, passes through the point (−1, 2.5) crossing the line, crosses the y-axis at approximately y = 1.3, becomes nearly horizontal at the approximate point (1, 1.2), goes down and right becoming more steep, passes through the point (2, 1) touching the line, crosses the x-axis at approximately x = 2.9, and exits the window in the fourth quadrant. The line enters the window in the second quadrant, goes down and right, passes through the point (−1, 2.5) crossing the curve, crosses the y-axis at y = 2, passes through the point (2, 1) touching the curve, crosses the x-axis at x = 4, and exits the window in the fourth quadrant. Point P occurs at (2, 1). Point A occurs at (−2, 3). (a)…
a) On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between them as obtained from the graph. b) Where is f(x) increasing on it's domain? c) Where is f(x) decresing on it's domain? e) At what x-value(s) would f(x) have a relative maximum? d) At what x-value(s) would f(x) have a relative minimum?
Consider the function h(x) = ((x^2) - x) / ((x + 1)^2), which has first derivative h'(x) = (3x - 1) / ((x + 1)^3) and second derivative h''(x) = (6 - 6x) / ((x + 1)^4). Find the vertical asymptotes, locate and classify all relative minima and maxima and point(s) of inflection. Give answers to 3 decimal places.
sketch the graph of y = x^3 / (x^2 - 4), keep in mind the information provided:1. x and y intercept: (0, 0)2. Vertical asymptotes: x = 2, x = -23. There is no horizontal asymptote.4. Discontinuity at x = -2 and x = 2.5. First derivative: y’ = (x^4 - 12x^2) / (x^2 - 4)^26. Critical points: x = 0, x = 2√3, x = -2√37. Intervals of increase: (-∞, -2√3) U (2√3, ∞)8. Intervals of decrease: (-2√3, -2) U (-2, 0)9. Local maxima: (-3.46, -5.20) and (3.46, 5.20)10. Second derivative: y’’ = (8x^3 + 96x) / (x^2 - 4)^311. Critical numbers: (0, 0), (√12, 3√3), (-√12, -3√3)12. Point of inflection: (0, 0)13. Concave upward: (-2, 0) U (2, ∞)14. Concave downward: (-∞, -2) U (0, 2) A sketch of the graph (by hand) - Labeling of vertical asymptotes on the sketch - Labeling of horizontal asymptotes on the sketch - Labeling of x and y intercepts on the sketch - Labeling of maximum and minimum points on the sketch - Labeling of points of inflection on the sketch A sketch of the graph on Desmos with all key…

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A function f(x) = x +b has vertical asymptotes at x=-2 and x=2. Given f'(x)= %3D Find: i) The values of a and b ii) The horizontal asymptote(s), critical point and inflection point(s), interval of increasing, decreasing, concave up and down, and finally sketch the graph.