for each problem, find the: x and y intercepts, x - coordinates of the critical points, open intervals where…

for each problem, find the: x and y intercepts, x - coordinates of the critical points, open intervals where the function is increasing and decreasing, x - coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. using this information, sketch the graph of the function.\n1) $y = -\frac{x^3}{3}+x^2$

for each problem, find the: x and y intercepts, x - coordinates of the critical points, open intervals where the function is increasing and decreasing, x - coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima. using this information, sketch the graph of the function.\n1) $y = -\frac{x^3}{3}+x^2$

Answer

Answer:

x - intercepts: (x = 0) and (x = 3); y - intercept: (y = 0); critical points: (x = 0) and (x = 2); increasing: ((0,2)); decreasing: ((-\infty,0)) and ((2,\infty)); inflection point: (x = 1); concave up: ((1,\infty)); concave down: ((-\infty,1)); relative minimum at (x = 0), relative maximum at (x = 2)