Y = 1-x ^ 2 find the decay function (derivative function)

In order to find the intervals of increase (decrease) of the function, it is necessary to find the zeros of the derivative and determine the signs of the resulting intervals.

y (x) = 1 – x ^ 2. Let’s find the derivative of this function:

y` (x) = -2x.

Find the zeros of the derivative: y` (x) = 0; -2x = 0; x = 0.

Let’s define the signs of each intral:

(-∞; 0) take x = -1; -2 * (-1) = 2. The derivative is positive, the function is increasing.

(0; + ∞) take x = 1; -2 * 1 = -2. The derivative is negative, the function decreases.

Answer: the function decreases on the interval (0; + ∞).