Question

How do you do this question?

Answer 1

Answer:

(-∞, -2), (-2, -0.618), and (1.618, 3)

Step-by-step explanation:

The red plus (+) signs indicate the regions in which the function is concave up, and the red negative (-) signs indicate the regions in which the function is concave down.

Note that the sign of the concavity changes at an inflection point.

Let's examine the intervals given.

(-∞, -2): Yes, concave up.

(-∞, -1.17): No. Concave up in (-∞, -2) but concave down in (-2, -1.17).

(-2, 0): No. Concave down in (-2, -1.17) but increasing in (-1.17, 0.0).

(-1.17, 0.689): Yes. Concave up.

(-0.618, 1.618): No. Concave up in (-0.618, 0.689) but concave down in (0.689, 1.618).

(0, 3): No. Concave up in (0, 0.689), concave down in (0.689, 2.481), and concave up in (2.481, 3).

(2.481, ∞): Yes. Concave up.

The three intervals that are concave up are (-∞, -2), (-1.17, -0.689), and (2.481, ∞).