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.

Question

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.

Accepted Answer

∻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.⚹◊What conditions must be satisfied for a point on a graph to be considered an inflection point of a twice differentiable function?⍭ Generate me a similar question◊

Sia