Okay, so this is a two part question here. Were given a graph off at prime and where has to approximate a slope of at and actually negative one now, because the slope is the driven, the function f every different point. We have to find ash prime of negative. Born using the graph of a crime. So we have to do is look up negative one. And it gets to you that this is approximately negative. One over two Part B asks us approximate any open intervals on which the graph of F is increasing and any organ it trickles and wished a graph of is decreasing. So we know that is F Crime of X is greater than zero for all acts. Then app is increasing so this implies that is increasing and similar. The crime of axe is less than zero. It implies that ass is decreasing on those intervals. So, as you can see on the graph after X is greater than zero for all acts in the range of negative too to infinity. And it is less than zero for all access in the range of native infinity, two native to all right. That's all

## Discussion

## Video Transcript

Okay, so this is a two part question here. Were given a graph off at prime and where has to approximate a slope of at and actually negative one now, because the slope is the driven, the function f every different point. We have to find ash prime of negative. Born using the graph of a crime. So we have to do is look up negative one. And it gets to you that this is approximately negative. One over two Part B asks us approximate any open intervals on which the graph of F is increasing and any organ it trickles and wished a graph of is decreasing. So we know that is F Crime of X is greater than zero for all acts. Then app is increasing so this implies that is increasing and similar. The crime of axe is less than zero. It implies that ass is decreasing on those intervals. So, as you can see on the graph after X is greater than zero for all acts in the range of negative too to infinity. And it is less than zero for all access in the range of native infinity, two native to all right. That's all

## Recommended Questions

HOW DO YOU SEE IT? Use the graph of $f^{\prime}$ shown in the figure to answer the following.

\begin{equation}\begin{array}{l}{\text { (a) Approximate the slope of } f \text { at } x=-1 . \text { Explain. }} \\ {\text { (b) Approximate any open intervals on which the }} \\ {\text { graph of } f \text { is increasing and any open intervals on }} \\ {\text { which it is decreasing. Explain. }}\end{array}\end{equation}

If a function is defined at $a, \lim _{x \rightarrow a} f(x)$ exists, but $\lim _{x \rightarrow a} f(x) \neq f(a),$ how is this shown on the function's graph?

Use the graph of the function $ f $ to state the value of each limit, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x \to 0^-}f(x) $

(b) $ \displaystyle \lim_{x \to 0^+}f(x) $

(c) $ \displaystyle \lim_{x \to 0}f(x) $

$ \displaystyle f(x) = \frac{1}{1+e^{1/x}} $

Use the graph of the function $ f $ to state the value of each limit, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x \to 0^-}f(x) $

(b) $ \displaystyle \lim_{x \to 0^+}f(x) $

(c) $ \displaystyle \lim_{x \to 0}f(x) $

$ \displaystyle f(x) = \frac{x^2 + x}{\sqrt{x^3 + x^2}} $

HOW DO YOU SEE IT? The graph of $f$ is

shown in the figure.

$$\begin{array}{l}{\text { (a) For which values of } x \text { is } f^{\prime}(x) \text { zero? Positive? }} \\ {\text { Negative? What do these values mean? }} \\ {\text { (b) For which values of } x \text { is } f^{\prime \prime}(x) \text { zero? Positive? }} \\ {\text { Negative? What do these values mean? }}\end{array}$$

$$\begin{array}{l}{\text { (c) On what open interval is } f^{\prime} \text { an increasing }} \\ {\text { function? }} \\ {\text { (d) For which value of } x \text { is } f^{\prime}(x) \text { minimum? For this }} \\ {\text { value of } x, \text { how does the rate of change of } f} \\ {\text { compare of } x \text { , how does the rate of change of } f} \\ {\text { values of } x ? \text { Explain. }}\end{array}$$

If you know that $\lim _{x \rightarrow c} f(x)$ exists, can you find its value by calculating $\lim _{x \rightarrow c^{+}} f(x) ?$ Give reasons for your answer.

Use the given graph of $ f $ to state the value of each quantity, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x\to 2^-}f(x) $

(b) $ \displaystyle \lim_{x\to 2^+}f(x) $

(c) $ \displaystyle \lim_{x\to 2}f(x) $

(d) $ f(2) $

(e) $ \displaystyle \lim_{x\to 4}f(x) $

(f) $ f(4) $

Use the graph of $f$ in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why.

a. $f(1) \quad$ b. $\lim _{T \rightarrow 1^{-}} f(x) \quad$ c. $\lim _{t \rightarrow 1^{+}} f(x)$

d. $\lim _{x \rightarrow 1} f(x)$

(GRAPH CAN'T COPY)

CAPSTONE Use the graph of the function $f$ to decide whether the value of the given quantity exists. If it does, find it. If not, explain why.

(a) $f(0)$

(b) $\lim_{x \to 0} f(x)$

(c) $f(2)$

(d) $\lim_{x \to 2} f(x)$

If a function is defined at $a,$ but $\lim _{x \rightarrow a} f(x)$ does not exist, how is this shown on the function's graph?