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Concave up and down intervals

User Flamenco
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1 Answer

17 votes
17 votes

Answer:

• (a)(1,∞).

,

• (b)(-∞,1).

,

• (c)(1,4)

Step-by-step explanation:

Consider the picture attached below:

Concave Up (Red Line)

When the tangent line lies below the graph, the graph is said to be Concave Up in the vicinity of that point.

Therefore, the interval where the graph is concave up is (1,∞).

Concave Down (Green Line)

When the tangent line lies above the graph, the graph is said to be Concave down in the vicinity of that point.

Therefore, the interval where the graph is concave down is (-∞.1).

Point of Inflection (Brown Line)

This is the point where the function changes from concave upward to concave downward or vice versa.

The point of inflection is (1,4)

Concave up and down intervals-example-1
User Russell Zornes
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2.8k points