Find the intervals of increasing, decreasing of the function, extremum points, type of extremum: y = 2×4-x3

Find the intervals of increase, decrease of the function, extremum points, type of extremum: y = 2 * x ^ 4 – x ^ 3;

1) intervals of increase, decrease of the function;

y = 2x ^ 4 – x ^ 3 = x ^ 3 (2 * x -1);

y = 0, x = 0 or x = 1/2 x belongs to (minus infinity; 0) union (1/2; + infinity)

the function will recover;

x belongs to (0; 1/2) function decreases;

2) points of extremum, type of extremum;

derivative = 8 * x ^ 3 – 3 * x ^ 2;

8 * x ^ 3-3 * x ^ 2 = 0;

x ^ 2 (8 * x – 3) = 0;

x = 0, x = 3/8;

y (0) = 0; y (3/8) = – 0.01;

at the point x = 3/8 the function has a minimum;