Question

Math

Posted 3 months ago

```
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}
```

Sign in to unlock the answer

Answer from Sia

Posted 3 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 $h$

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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question