Solving and sketching the graph of a polynomial function using Mathematical Software (Maple Software) 1 2 3 4 Define the function f(x) = 4x - 24x+36x Find the i) x-intercept ii) y-intercept Find the critical points using the following steps: i) Differentiate f ii) Factorize" iii) Solve f' = 0 (determine x and X iv) Find f(x) v) Find f(x) Find the interval(s) where f is increasing or decreasing using the following steps: i) ii) Find the first derivative and denote it by Determine the interval(s) on which is increasing (f(x) > 0) or decreasing (f(x) 0 or 0) and concave down (f(x) < 0) by substituting a test value from each interval. i) ii) Sketch the graph off by drawing a curve that passes through the critical points and the inflection point. Label the critical points, the inflection point, minimum and maximum point. Minimum point: Maximum point: On which interval isf concave up On which interval is concave down State the inflection point