# Examine the function y = -5x ^ 2-4x + 11 for monotonicity.

July 24, 2021 | education

| In order to find the intervals on which the function y = -5x ^ 2 – 4x + 11 monotonically increases or decreases, we will act as follows.

Let’s remember what kind of graph a given function has. The graph is a parabola whose branches are directed downward.

The vertex of the parabola is its highest value. And the intervals from – infinity to the top of the parabola and from the top of the parabola to + infinity are intervals of monotonicity – increasing and decreasing, respectively.

We are looking for the top of the parabola:

x0 = -b / 2a = – (- 4) / 2 * (-5) = 4 / -10 = -2/5.

Increases: (-infinity; -2/5). Decreases: (-2/5; + infinity).

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