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 ⋮ To determine the inflection points of the function $h$, we need to find where the second derivative $h''(x)$ changes sign. ‖ ‖ step 2 ⋮ An inflection point occurs where the concavity of the function changes, which means $h''(x)$ must be zero or undefined at that point, and the sign of $h''(x)$ must change around that point. ‖ ‖ step 3 ⋮ Observing the graph, we need to identify points where the curve changes from concave up to concave down or vice versa. ‖ ‖ step 4 ⋮ Point A: The curve changes from concave down to concave up, indicating an inflection point. ‖ ‖ step 5 ⋮ Point B: The curve does not change concavity, so it is not an inflection point. ‖ ‖ step 6 ⋮ Point C: The curve does not change concavity, so it is not an inflection point. ‖ ‖ step 7 ⋮ Point D: The curve changes from concave up to concave down, indicating an inflection point. ‖ ***A, D*** ∻Key Concept∻ ⚹Inflection Points⚹ ∻Explanation∻ ⚹Inflection points occur where the second derivative of a function changes sign, indicating a change in concavity.⚹◊What is the definition of an inflection point in calculus?⍭ Generate me a similar question◊

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