Graph Analysis

The graph below shows the function $y=f(x)$.

(i) For the function above, find the value(s) of $x$ where $f(x)$ is continuous but not
differentiable.

(ii) For the function above, find the value(s) of $x$ where $f^{\prime }(x)=0$.

(iii) What is the value of ${\lim }_{x\to -1}f(x)$?

State clearly if the value does not exist.

The graph below shows the function $y=f(x)$.

For the function above:
(i) Find the value(s) of $x$ where $f(x)$ is continuous but not differentiable.

(ii) Find the value(s) of $x$ where $f^{\prime }(x)=0$ and $f^{\prime \prime }(x)<0$ are both true.

(iii) What is the value of ${\lim }_{x\to 6}f(x)$?

State clearly if the value does not exist.

The graph below shows the function $y=f(x)$.

For the function above:
(i) Find the value(s) of $x$ where $f(x)$ is not differentiable.

(ii) Find the value(s) of $x$ for which $f^{\prime }(x)=0$.

(iii) What is the value of $\underset{x\to -4}{\lim }f(x)$?
(State clearly if the value does not exist.)

The graph below shows the function $y=f(x)$.

For the function above:

(i) Find the value(s) of $x$ that meet the following conditions:

(1) $f^{\prime }(x)=0$:

(2) $f(x)$ is concave upwards:

(ii) What is the value of ${\lim }_{x\to 7}f(x)$:

State clearly if the value does not exist.

The graph below shows the function $y=f(x)$.

(i) Find all the value(s) of $x$ which meet each of the following conditions:

1. $f^{\prime }(x)=0$:

2. $f(x)$ is not differentiable:

(ii) What is the value of ${\lim }_{x\to 1}f(x)$?

State clearly if the value does not exist.

The diagram below shows the graph of the function $y=f(x)$.

For the function above:

(i) What is the value of $f(1)$?
State clearly if the value does not exist.

(ii) For what value(s) of $x$ does the function $f(x)$ not have a limit?

(iii) Find all the value(s) of $x$ that meet the following conditions:

(1) $f^{\prime }(x)>0$:

(2) $f^{\prime }(x)=0$ and $f^{\prime \prime }(x)<0$:

(3) $f(x)$ is continuous but not differentiable:

The graph below shows the function $y=f(x)$.

For the function above:
(i) Find the value(s) of $x$ that meet the following conditions:
(1) $f^{\prime }(x)=0$:
(2) $f(x)$ is continuous but not differentiable:
(3) $f(x)$ is not continuous:
(4) $f^{\prime \prime }(x)<0$:

(ii) What is the value of ${\lim }_{x\to -1}f(x)$?
State clearly if the value does not exist.

The graph below shows the function $y=f(x)$.

For the function $y=f(x)$ above:

(i) Find the value(s) of $x$ that meet the following conditions:

1. $f$ is not continuous:

2. $f$ is not differentiable:

3. $f^{\prime }(x)=0$:

4. $f^{\prime \prime }(x)<0$:

(ii) What is the value of ${\lim }_{x\to -1}f(x)$?
State clearly if the value of the limit does not exist.

The graph below shows the function $y=f(x)$.

For the function above:

(i) Find the value(s) of $x$ that meet the following conditions:

1. $f(x)$ is not defined:

2. $f(x)$ is not differentiable:

3. $f^{\prime \prime }(x)>0$:

(ii) What is the value of $f(-1)$?

State clearly if the value does not exist.

(iii) What is the value of ${\lim }_{x\to 2}f(x)$?

State clearly if the value does not exist.

The graph below shows the function $y=f(x)$.

For the function $f(x)$ above:

(i) Find the value(s) for $x$ that meet the following conditions:

1. $f(x)$ is not differentiable: ______________________________

2. $f^{\prime \prime }(x)<0$: ______________________________

3. $f(x)$ is not defined: ______________________________

(ii) What is the value of $f(2)$? ______________________________

*State clearly if the value does not exist.*

(iii) What is the value of ${\lim }_{x\to -1}f(x)$? ______________________________

*State clearly if the value does not exist.*

The graph below shows the function $y=f(x)$.

For the function $f(x)$ above:

(i) Find all the value(s) of $x$ that meet each of the following conditions:

1. $f^{\prime }(x)=0$

2. $f^{\prime \prime }(x)<0$

3. $f(x)$ is not differentiable

(ii) What is the value of $f(-1)$?

(iii) What is the value of ${\lim }_{x\to 3}f(x)$?

State clearly if the value does not exist.