Question

Math

Posted 3 months ago

```
Let $h$ be a twice differentiable function.
Which of the labeled points are inflection points of $h$ ?
Choose all answers that apply:
A $A$
B $B$
C $C$
D $D$
E The graph has no inflection points.
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

We need to determine the inflection points of the function $h$ based on the given graph. Inflection points occur where the concavity of the function changes, which corresponds to where the second derivative $h''(x)$ changes sign

step 2

From the graph, we observe the following:
- Point A is near the maximum of the function in the second quadrant.
- Point B is near the local minimum of the function in the third quadrant.
- Point C is on the x-axis.
- Point D is in the fourth quadrant as the function is increasing.
To identify inflection points, we need to look for points where the concavity changes

step 3

At Point A, the function changes from concave up to concave down, indicating a possible inflection point

step 4

At Point B, the function changes from concave down to concave up, indicating another possible inflection point

step 5

At Point C, the function does not show a change in concavity

step 6

At Point D, the function does not show a change in concavity

step 7

Therefore, the inflection points are at Points A and B

Answer

Points A and B

Key Concept

Inflection Points

Explanation

Inflection points occur where the second derivative of a function changes sign, indicating a change in concavity.

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