$$ y=\frac{6\left(x^{2}-1\right)}{x^{2}+3} \quad \underline{\text { Note }}: y^{\prime}=\frac{48 x}{\left(x^{2}+3\right)^{2}}, \quad y^{\prime \prime}=\frac{144\left(1-x^{2}\right)}{\left(x^{2}+3\right)^{3}} $$
Sketch the graph of each of the following, giving intercepts, asymptotes, where increasing. where decreasing, any relative maximum and relative minimum points, where concave upward, where concave downward, and any inflection points.
Sketch the graph of each of the following, giving intercepts, asymptotes, where increasing. where decreasing
Find where the graph of f is increasing, decreasing, concave upward and concave downward then find any intercepts, relative extrema, points of inflection, and asymptote. Use this information to sketch the graph of f.f(x) = (2x-1)2(x-3) (x-7)
4. For the following function f find the domain; the asymptotes ;intervals where f is increasing, decreasing, concave upward, concave downward; local maximum, minimum and inflection points; sketch the graph: f(x) = 1/(x-1)3
Analyze and sketch the graph of each function. Local intercepts, relative extrema, points of inflection and asymptotes. State for each problem the following: domain, range, intercepts, symmetry, asymptotes (horizontal and/or vertical asymptotes), critical numbers, points of inflection. a. \(Y=x^{2}+1 / x^{2}-9\)b. \(Y=x^{2} / x^{2}+3\)c. \(\mathrm{Y}=\frac{1}{3}\left(x^{2}-3 x+2\right)\)d. \(\mathrm{F}(\mathrm{x})=\frac{1}{x e^{x}}\)e. \(F(x)=x^{5}-5 x\)
Sketch the graph of the following function. State where any intercepts occur, where asymptotes occur, where any relative extrema occur, where the function is increasing or decreasing, where any inflection points occur, and where the graph is concave up or concave down. 22 x² - 4 Determine the x-intercept(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA (Simplify your answer. Type an ordered pair Use integers or fractions for any...
Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. X +3 f(x) = x²-x-12 On what interval(s) is fincreasing and on what interval(s) is f decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The...
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) x25 y= x2-64 intercept (x, y)- relative minimum (x, y)- relative maximum (x, y) point of inflection (x, y)- Find the equations of the asymptotes. (smaller x-value) (larger x-value) (horizontal asymptote) Use a graphing utility to verify your results. O 1/8 points Previous Answers LarCalc9 3.6.009. Analyze and sketch a graph of the function....
Sketch the graph of f(x)= (x^2)/(x^2-1), stating all relative extreme points, intervals of increasing and decreasing, intervals of concave up and concave down, inflection points, and asymptotes.
Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. 1. y = 2
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer y = x + 1 intercept (x, y) = -1.0 relative minimum (x, y) = ( I relative maximum (x, y) = points of inflection (x, y) = (smallest x-value) (x, y) = (x, y) = (largest x-value) Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations.) Use a graphing utility to verify...
Can please help on how to simply the derivative I get lost on part c Name: (3) Consider the graph of the function 5e-3 (a) Find the z- and y-intercepts of the graph, if any. The answers are equa f(z) = tions, not numbers. (b) Find the horizontal and vertical asymptotes of the graph, if any. The answers are equations, not numbers. (c) Where is f(x) increasing? ...decreasing? The answers are intervals. (d) Where is f(x) concave up? concave down?...