Find the intervals of increasing and decreasing of the function: y = 0.25x ^ 4- 0.5x ^ 2-1

Let’s find the derivative of the function:

y ‘= (0.25x ^ 4 – 0.5x ^ 2 – 1)’ = 0.5x ^ 3 – x.

We equate it to zero and find the extrema of the function:

0.5x ^ 2 – x = 0;

x * (0.5x – 1) = 0;

x1 = 0; x2 = 2.

Since y ‘> 0 on the intervals from infinity to 0 and from 2 to infinity – the function increases, on the interval (0; 2) y’ <0 – the interval of decrease of the function.