Examine the function for monotonicity y = 5x ^ 2-4x + 1.

Given a function:

y = 5 * x ^ 2 – 4 * x + 1.

To find the intervals of increase and decrease, we find the derivative of the function:

y ‘= 10 * x – 4.

The function increases where its derivative is greater than zero, and decreases where the derivative is negative.

We solve the inequality:

10 * x – 4> 0;

10 * x> 4;

x> 2/5 – interval of increasing function.

Accordingly, x <2/5 is the interval of decreasing function.