FUNCTION: f(x) = 2x^2-3x+6/5/3x^2+5x-2 Determine the domain of f(x). Write your
ID: 3288808 • Letter: F
Question
FUNCTION: f(x) = 2x^2-3x+6/5/3x^2+5x-2 Determine the domain of f(x). Write your answer in the Curve Sketching table provided. Test for any symmetry in the function. Indicate if you discovered any symmetries in the Curve Sketching table. Test for any points of discontinuity. Indicate these points and their type on the Curve Sketching table. Analyse the results from the previous question to determine where the vertical asymptotes are located (if any). Indicate any vertical asymptotes that you found on the Curve Sketching table. Determine where f(x) changes sign. Use these locations to create intervals and determine whether f(x) is positive or negative in these intervals. Indicate this information on the Curve Sketching table. Using the information from the previous question, indicate where the x-intercepts for f(x) are located (if any) in the Curve Sketching table. Determine if f(x) has any horizontal asymptotes. Indicate any horizontal asymptote that you find in the Curve Sketching table. Calculate f '(x). Calculate the critical numbers for f (x). Using the critical numbers from the previous question, separate the x-axis into intervals to use for determining where f '(x) changes sign. Choose arbitrary points in each interval and then use Maple to calculate the value of f '(x) at these arbitrary points. Using the results, indicate whether f o(x) is positive or negative in these intervals, and whether this means that f(x) is increasing or decreasing. Summarize this information in the space provided in the Curve Sketching table. Using the information from the previous question, determine whether the critical numbers are local maxima, local minima or neither. If a critical number is a local maxima or a local minima, Write the coordinates of the maxima and minima (if any) in the space provided on the Curve Sketching table. Calculate f "(x). Calculate the critical numbers for the second derivative, f "(x). Using the critical numbers from the previous question, separate the x-axis into intervals to use for determining where f "(x) changes sign. Choose arbitrary points in each interval and then use Maple to calculate the value of f "(x) at these arbitrary points. Using the results, indicate whether f oo(x) is positive or negative in these intervals, and whether this means that f(x) is concave up or concave down. Summarize this information in the space provided in the Curve Sketching table. Using the informaton from the previous question, determine whether the critical numbers are points of inflection. If a critical number is a point of inflection, use Maple to find the y-coordinate of the point. Write the coordinates of the points of inflection (if any) in the space provided on the Curve Sketching table. Using the information in the Curve Sketching table, create the sketch of the graph of f(x) on the graph paper provided. You can indicate appropriate intervals of your own choice for the x- and y-axis. Label each element of the graph (for example, provide the coordinates of each point you plotted, label maxima, minima, points of inflection, asymptotes, etc. Also, indicate on the graph where f(x) is positive or negative, increasing or decreasing, and concave upward or downward. Create the plot of this function with x and y both ranging from -10.. 10. If the plot does not match your sketch, review your calculations to determine where you have made an error.Explanation / Answer
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