Find local maximum of g(x), use the second derivative test to justify your answer. g(x) = x² + x³ 3x² 2x + 1 (a) Define the function g(x) and the function will be plotted automatically. 2 (b) Calculate the first and the second derivative of g(x). If you assign names to these functions, if will be easier to use them in the following steps. (c) Use Solve command to find the critical points. Note that the equation obtained at this step cannot be solved analytically, so the use of Geogebra is essential. (d) Use the second derivative test to find which of the critical point is the relative maximum. (e) Find the relative maximum of g(x). (f) Save a screenshot of your calculations in (a)-(e) and submit it for your assign- ment; include the graph of g(x) in your screenshot.