9514 1404 393
Answer:
concave up: (-3, ∞)
concave down: (-∞, -3)
inflection point: (-3, -4)
Step-by-step explanation:
The inflection point of a cubic is halfway between the turning points. Those are at (-4.5, -2) and (-1.5, -6). So, the point of inflection is ...
((-4.5, -2) +(-1.5, -6))/2 = (-6, -8)/2 = (-3, -4) . . . point of inflection
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In order to determine concave up/down intervals, you need to know where the point of inflection is. For a cubic like this one with a positive leading coefficient, the concave down interval is to the left of the inflection point. The curve is concave up to the right of the inflection point. So, the intervals of interest are ...
concave up: (-3, ∞)
concave down: (-∞, -3)
inflection point: (-3, -4)
