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Question
Math
Posted 6 months ago

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

Choose the option that matches each function with its appropriate graph.
Choose 1 answer:
(A) A hhh\quad h \quad h^{\prime} \quad h^{\prime \prime}
I II III
(B) Bhhh\mathrm{B} \quad h \quad h^{\prime} \quad h^{\prime \prime}
I III II
(C) Chhh\mathrm{C} \quad h \quad h^{\prime} \quad h^{\prime \prime}
II III I
(D)
\begin{tabular}{|llll|}
\hline D\mathrm{D} & hh & hh^{\prime} & hh^{\prime \prime} \\
\hline & III & II & I \\
&
\end{tabular}
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Answer from Sia
Posted 6 months ago
Solution by Steps
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 hh
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 hh'
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 hh''
step 5
Match the graphs to the functions: hh corresponds to Graph I, hh' corresponds to Graph II, and hh'' 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.

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