Let $h$ be a twice differentiable function except at a vertical asymptote. One of these graphs is the graph of $h$, one is of $h^{\prime}$ and one is of $h^{\prime \prime}$.

Choose the option that matches each function with its appropriate graph.
Choose 1 answer:
(A) A $\quad h \quad h^{\prime} \quad h^{\prime \prime}$
I II III
(B) $\mathrm{B} \quad h \quad h^{\prime} \quad h^{\prime \prime}$
I III II
(C) $\mathrm{C} \quad h \quad h^{\prime} \quad h^{\prime \prime}$
II III I
(D)
\begin{tabular}{|llll|}
\hline $\mathrm{D}$ & $h$ & $h^{\prime}$ & $h^{\prime \prime}$ \
\hline & III & II & I \
&
\end{tabular}

Question

Let $h$ be a twice differentiable function except at a vertical asymptote. One of these graphs is the graph of $h$, one is of $h^{\prime}$ and one is of $h^{\prime \prime}$.

Choose the option that matches each function with its appropriate graph.
Choose 1 answer:
(A) A $\quad h \quad h^{\prime} \quad h^{\prime \prime}$
I II III
(B) $\mathrm{B} \quad h \quad h^{\prime} \quad h^{\prime \prime}$
I III II
(C) $\mathrm{C} \quad h \quad h^{\prime} \quad h^{\prime \prime}$
II III I
(D)
\begin{tabular}{|llll|}
\hline $\mathrm{D}$ & $h$ & $h^{\prime}$ & $h^{\prime \prime}$ \
\hline & III & II & I \
&
\end{tabular}

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the behavior of each graph to determine which represents $h$, $h'$, and $h''$. ‖ ‖ step 2 ⋮ Graph I: The curve decreases, passes through the y-axis, continues to decrease until it gets close to the vertical asymptote, then increases after the asymptote. This behavior suggests it could be the original function $h$. ‖ ‖ step 3 ⋮ Graph II: The curve increases, passes through the y-axis, continues to increase until it gets close to the vertical asymptote, then decreases after the asymptote. This behavior suggests it could be the first derivative $h'$. ‖ ‖ step 4 ⋮ Graph III: The curve decreases, continues to decrease until it gets close to the vertical asymptote, then decreases again after the asymptote. This behavior suggests it could be the second derivative $h''$. ‖ ‖ step 5 ⋮ Match the graphs to the functions: $h$ corresponds to Graph I, $h'$ corresponds to Graph II, and $h''$ corresponds to Graph III. ‖ ***A*** ∻Key Concept∻ ⚹Matching functions and their derivatives to graphs⚹ ∻Explanation∻ ⚹By analyzing the behavior of each graph, we can determine which graph represents the original function, its first derivative, and its second derivative.⚹◊What mathematical properties can be inferred about a function and its derivatives based on their corresponding graphs?⍭ Generate me a similar question◊

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