Use methods of algebra and calculus to analyze the graph of the function. f(x)=-x^3-x+5/2x^3+3x^2-7. Include all the following in your analysis: a)the domain b)interceptsc)equations of asymptotes (both vertical and horizontal)d)relative extrema (be sure to provide all derivatives, identify critical numbers, and show the test for those values – naming the test you are using.)g, ye)intervals where the function is increasing or decreasing f)inflection points (be sure to identify possible inflection points and be sure to show the test for those values.)g)intervals where the graph is concave up and where it is concave down (be sure to include the vertical asymptotes in your intervals.) h)provide computer-generated graphs of your function that illustrate all of the key points that you have listed. You may need to provide more than one graph.