Find the intervals of increasing and decreasing of the function: y = x ^ 2-6x.

Find the gaps using the derivative. The function increases in the interval where its derivative takes positive values, and decreases – where the derivative takes negative values.

y ‘= (x ^ 2 – 6x)’ = 2x – 6.

Find the zeros of the function.

2x – 6 = 0;

2x = 6;

x = 6: 2;

x = 3.

Mark on the number line point 3, which divides it into two intervals: 1) (-∞; 3), 2) (3; + ∞). On the first interval, the derivative 2x – 6 takes negative values, and on the second – positive. This means that in the first interval the function y = x ^ 2 – 6x decreases, and in the second it increases.

Answer. Decreases by (-∞; 3); increases by (3; + ∞).