Question 1

Suppose a function is given by a table of values as follows:
 $\begin{array}{ccccccc}
x & 1.1 & 1.3 & 1.5 & 1.7 & 1.9 & 2.1 \
f(x) & 14 & 17 & 23 & 25 & 26 & 27
\end{array}$ Give your best estimate of $f^{\prime \prime}(1.9)$
 .

Accepted Answer

The answer of Suppose a function is given by a...

Question 2

Let $f(x)=x^{-2 / 3}$ .Use a graph to decide which one of the following statements is true.

Accepted Answer

A) When x = -5, the derivative is negative; when x = 5, the derivative is positive; and as x approaches infinity, the derivative approaches 0. 
B) When x = -6, the derivative is positive; when x = 6, the derivative is also positive, and as x approaches infinity, the derivative approaches 0. 
C) When x = -7, the derivative is negative; when x = 7, the derivative is positive, and as x approaches infinity, the derivative approaches infinity. 
D) The derivative is positive at at all values of x. 
A) When x = -5, the derivative is negative; when x = 5, the derivative is positive; and as x approaches infinity, the derivative approaches 0. 
B) When x = -6, the derivative is positive; when x = 6, the derivative is also positive, and as x approaches infinity, the derivative approaches 0. 
C) When x = -7, the derivative is negative; when x = 7, the derivative is positive, and as x approaches infinity, the derivative approaches infinity. 
D) The derivative is positive at at all values of x.

Question 3

Based on the graph of f(x)below:
a)List all values of x for which f is NOT differentiable.
b)List all values of x for which f is NOT continuous.
c)List all values of x for which f '(x)= 0.

Accepted Answer

a)Not differentiable at x = -2

Question 4

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 17.00 meters per second and will attain a height of $s(t)=-0.8 t^{2}+17.00 t$
 meters in t seconds.Find a formula for the velocity of the golf ball at time t.

Accepted Answer

A)  $v(t)=-1.6 t+17.00$
 meters/sec 
B)  $v(t)=-0.8 t+8.50$
   meters/sec 
C)  $v(t)=$
 -1.36 meters/sec 
D)  $v(t)=-16 t^{2}+17.00$
 meters/sec 
A)  $v(t)=-1.6 t+17.00$
 meters/sec 
B)  $v(t)=-0.8 t+8.50$
   meters/sec 
C)  $v(t)=$
 -1.36 meters/sec 
D)  $v(t)=-16 t^{2}+17.00$
 meters/sec

Question 5

For $f(x)=\log x$
 , estimate f '(3)to 3 decimal places by finding the average slope over intervals containing the value x = 3.

Accepted Answer

The answer of For $f(x)=\log x$
 , estimate f '(3)to...

Question 6

A typhoon is a tropical cyclone, like a hurricane, that forms in the northwestern Pacific Ocean.The wind speed of a typhoon is given by a function W = w(r)where W is measured in meters/sec., and r is measured in kilometers from the center of the typhoon.What does the statement that w'(15)> 0 tell you about the typhoon?

Accepted Answer

A) At a distance of 15 kilometers from the center of the typhoon, the wind speed is increasing. 
B) At a distance of 15 kilometers from the center of the typhoon, the wind speed is positive. 
C) The wind speed of the typhoon is 15 meters per second at any distance from the center of the typhoon. 
A) At a distance of 15 kilometers from the center of the typhoon, the wind speed is increasing. 
B) At a distance of 15 kilometers from the center of the typhoon, the wind speed is positive. 
C) The wind speed of the typhoon is 15 meters per second at any distance from the center of the typhoon.

Question 7

A runner competed in a half marathon in Anaheim, a distance of 13.1 miles.She ran the first 7 miles at a steady pace in 48 minutes, the second 3 miles at a steady pace in 28 minutes and the last 3.1 miles at a steady pace in 18 minutes.
a)Sketch a well-labeled graph of her distance completed with respect to time.
b)Sketch a well-labeled graph of her velocity with respect to time.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Answers will vary.

Question 8

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 14.00 meters per second and will attain a height of $s(t)=-0.8 t^{2}+14.00 t$
 meters in t seconds.What is the acceleration of the golf ball at time t?

Accepted Answer

A)  -1.6 meters/sec/sec 
B)  -1.6t meters/sec2 
C)  -0.8t meters/sec/sec 
D) 14.00 meters/sec2 
A)  -1.6 meters/sec/sec 
B)  -1.6t meters/sec2 
C)  -0.8t meters/sec/sec 
D) 14.00 meters/sec2

Question 9

The graph below represents the rate of change of a function f with respect to x; i.e., it is a graph of f '.You are told that f (0)= 0.What can you say about $f(x)$
 at the point x = 1.3? Mark all that apply.

Accepted Answer

A)  $f(x)$ is decreasing. 
B)  $f(x)$
 is increasing. 
C)  $f(x)$
 is concave up. 
D)  $f(x)$
 is concave down. 
A)  $f(x)$ is decreasing. 
B)  $f(x)$
 is increasing. 
C)  $f(x)$
 is concave up. 
D)  $f(x)$
 is concave down.

Question 10

On the axes below, sketch a smooth, continuous curve , and which clearly satisfies the following conditions:
• Concave up to the left of P
• Concave down to the right of P
• Increasing for x > 0
• Decreasing for x < 0
• Does not pass through the origin.

Accepted Answer

Answers wi

Question 11

Assume that f is a differentiable function defined on all of the real line.Is it possible that f > 0 everywhere, f ' > 0 everywhere, and f ' < 0 everywhere?

Accepted Answer

A) True 
 B)False

Question 12

A company graphs C'(t), the derivative of the number of pints of ice cream sold over the past ten years.At approximately what year was C ''(t)greatest?

Accepted Answer

The answer of A company graphs C'(t), the derivative of...

Question 13

The graph of $f(x)$
 is given in the following figure.What happens to $f^{\prime}(x)$
 at the point $x_{1}$
 ?

Accepted Answer

A)  $f^{\prime}(x)$
 has an inflection point. 
B)  $f^{\prime}(x)$
 has a local minimum or maximum. 
C)  $f^{\prime}(x)$
 changes sign. 
D) none of the above 
A)  $f^{\prime}(x)$
 has an inflection point. 
B)  $f^{\prime}(x)$
 has a local minimum or maximum. 
C)  $f^{\prime}(x)$
 changes sign. 
D) none of the above

Question 14

The graph below shows the velocity of a bug traveling along a straight line on the classroom floor.   At what time(s)does the bug turn around?

Accepted Answer

A) At 3 seconds. 
B) At 2 seconds and again at 7 seconds. 
C) At 4 seconds and again at 7 seconds. 
D) Never. 
A) At 3 seconds. 
B) At 2 seconds and again at 7 seconds. 
C) At 4 seconds and again at 7 seconds. 
D) Never.

Question 15

Esther is a swimmer who prides herself in having a smooth backstroke.Let s(t)be her position in an Olympic size (50-meter)pool, as a function of time (s(t)is measured in meters, t is seconds).Below we list some values of s(t), for a recent swim.Based on the data, was Esther's instantaneous speed ever greater than 3 meters/second?
 $$\begin{array} { c c c c c c c c c c c c } 
t & 0 & 3.0 & 8.6 & 14.6 & 20.8 & 27.6 & 31.9 & 38.1 & 45.8 & 53.9 & 60 \
s ( t ) & 0 & 10 & 20 & 30 & 40 & 50 & 40 & 30 & 20 & 10 & 0
\end{array}$$

Accepted Answer

The answer of Esther is a swimmer who prides herself...

Question 16

Is the function $f(x)=\frac{x^{2}|2 x-4|}{x-2}$
 continuous at x = 2?

Accepted Answer

A) True 
 B)False

Question 17

To find the derivative of $g(x)=2 x^{2}+5 x-9$
 at x = 8 algebraically, you evaluate the following expression.

Accepted Answer

A)  $\lim _{h \rightarrow 0} \frac{2(8+h)^{2}-5(8+h)-9-\left(2 \cdot 8^{2}+5 \cdot 8-9\right)}{h}$ 
B)  $\frac{g(8+1)+g(8)}{h}$ 
C)  $\lim _{h \rightarrow \infty} \frac{g(h)-g(8)}{h}$ 
D) All of the above are correct. 
E) None of the above is correct. 
A)  $\lim _{h \rightarrow 0} \frac{2(8+h)^{2}-5(8+h)-9-\left(2 \cdot 8^{2}+5 \cdot 8-9\right)}{h}$ 
B)  $\frac{g(8+1)+g(8)}{h}$ 
C)  $\lim _{h \rightarrow \infty} \frac{g(h)-g(8)}{h}$ 
D) All of the above are correct. 
E) None of the above is correct.

Question 18

Is the graph of $f(x)=|x+3|$
 continuous at x = -3?

Accepted Answer

A) True 
 B)False

Question 19

The graph below represents the rate of change of a function f with respect to x; i.e., it is a graph of f'.You are told that f(0)= -2.For approximately what value of x other than x = 0 in the interval 0 $\le$ x $\le$ 2 does $f(x)$
 = -2?

Accepted Answer

A) 0.6 
B) 1 
C) 1.4 
D) 2 
E) None of the above 
A) 0.6 
B) 1 
C) 1.4 
D) 2 
E) None of the above

Question 20

To study traffic flow along a major road, the city installs a device at the edge of the road at 3:00a.m.The device counts the cars driving past, and records the total periodically.The resulting data is plotted on a graph, with time (in hours since installation)on the horizontal axis and the number of cars on the vertical axis.The graph is shown below; it is the graph of the function C(t)= Total number of cars that have passed by after t hours.From the graph, estimate C'(6).

Accepted Answer

A) 600 
B) 900 
C) 1200 
D) 1500 
A) 600 
B) 900 
C) 1200 
D) 1500

Suppose a function is given by a table of values as follows: x 1.1 1.3 1.5 1.7 1.9 2.1 f(x) 14 17 23 25 26 27 Give your best estimate of $f^{\prime \prime}(1.9)$ .

Let $f(x)=x^{-2 / 3}$ .Use a graph to decide which one of the following statements is true.

Based on the graph of f(x)below: a)List all values of x for which f is NOT differentiable. b)List all values of x for which f is NOT continuous. c)List all values of x for which f '(x)= 0.

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 17.00 meters per second and will attain a height of $s(t)=-0.8 t^{2}+17.00 t$ meters in t seconds.Find a formula for the velocity of the golf ball at time t.

For $f(x)=\log x$ , estimate f '(3)to 3 decimal places by finding the average slope over intervals containing the value x = 3.

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 14.00 meters per second and will attain a height of $s(t)=-0.8 t^{2}+14.00 t$ meters in t seconds.What is the acceleration of the golf ball at time t?

The graph below represents the rate of change of a function f with respect to x; i.e., it is a graph of f '.You are told that f (0)= 0.What can you say about $f(x)$ at the point x = 1.3? Mark all that apply.

On the axes below, sketch a smooth, continuous curve , and which clearly satisfies the following conditions: • Concave up to the left of P • Concave down to the right of P • Increasing for x > 0 • Decreasing for x < 0 • Does not pass through the origin.

Assume that f is a differentiable function defined on all of the real line.Is it possible that f > 0 everywhere, f ' > 0 everywhere, and f ' < 0 everywhere?

A company graphs C'(t), the derivative of the number of pints of ice cream sold over the past ten years.At approximately what year was C ''(t)greatest?

The graph below shows the velocity of a bug traveling along a straight line on the classroom floor. At what time(s)does the bug turn around?

Is the function $f(x)=\frac{x^{2}|2 x-4|}{x-2}$ continuous at x = 2?

To find the derivative of $g(x)=2 x^{2}+5 x-9$ at x = 8 algebraically, you evaluate the following expression.

Is the graph of $f(x)=|x+3|$ continuous at x = -3?

A Library of Functions

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Constructing Antiderivatives

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Exam 2: Key Concept: the Derivative

Suppose a function is given by a table of values as follows: x 1.1 1.3 1.5 1.7 1.9 2.1 f(x) 14 17 23 25 26 27 Give your best estimate of f′′(1.9)f^{\prime \prime}(1.9)f′′(1.9) .

Let f(x)=x−2/3f(x)=x^{-2 / 3}f(x)=x−2/3 .Use a graph to decide which one of the following statements is true.

Based on the graph of f(x)below: a)List all values of x for which f is NOT differentiable. b)List all values of x for which f is NOT continuous. c)List all values of x for which f '(x)= 0.

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 17.00 meters per second and will attain a height of s(t)=−0.8t2+17.00ts(t)=-0.8 t^{2}+17.00 ts(t)=−0.8t2+17.00t meters in t seconds.Find a formula for the velocity of the golf ball at time t.

For f(x)=log⁡xf(x)=\log xf(x)=logx , estimate f '(3)to 3 decimal places by finding the average slope over intervals containing the value x = 3.

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 14.00 meters per second and will attain a height of s(t)=−0.8t2+14.00ts(t)=-0.8 t^{2}+14.00 ts(t)=−0.8t2+14.00t meters in t seconds.What is the acceleration of the golf ball at time t?

The graph below represents the rate of change of a function f with respect to x; i.e., it is a graph of f '.You are told that f (0)= 0.What can you say about f(x)f(x)f(x) at the point x = 1.3? Mark all that apply.

On the axes below, sketch a smooth, continuous curve , and which clearly satisfies the following conditions: • Concave up to the left of P • Concave down to the right of P • Increasing for x > 0 • Decreasing for x < 0 • Does not pass through the origin.

Assume that f is a differentiable function defined on all of the real line.Is it possible that f > 0 everywhere, f ' > 0 everywhere, and f ' < 0 everywhere?

A company graphs C'(t), the derivative of the number of pints of ice cream sold over the past ten years.At approximately what year was C ''(t)greatest?

The graph of f(x)f(x)f(x) is given in the following figure.What happens to f′(x)f^{\prime}(x)f′(x) at the point x1x_{1}x1​ ?

The graph below shows the velocity of a bug traveling along a straight line on the classroom floor. At what time(s)does the bug turn around?

Is the function f(x)=x2∣2x−4∣x−2f(x)=\frac{x^{2}|2 x-4|}{x-2}f(x)=x−2x2∣2x−4∣​ continuous at x = 2?

To find the derivative of g(x)=2x2+5x−9g(x)=2 x^{2}+5 x-9g(x)=2x2+5x−9 at x = 8 algebraically, you evaluate the following expression.

Is the graph of f(x)=∣x+3∣f(x)=|x+3|f(x)=∣x+3∣ continuous at x = -3?

The graph below represents the rate of change of a function f with respect to x; i.e., it is a graph of f'.You are told that f(0)= -2.For approximately what value of x other than x = 0 in the interval 0 ≤\le≤ x ≤\le≤ 2 does f(x)f(x)f(x) = -2?

A Library of Functions

Short-Cuts to Differentiation

Using the Derivative

Key Concept- the Definite Integral

Constructing Antiderivatives

Integration

Using the Definite Integral

Sequences and Series

Approximating Functions Using Series

Differential Equations

Functions of Several Variables

A Fundamental Tool- Vectors

Differentiating Functions of Several Variables

Optimization- Local and Global Extrema

Integrating Functions of Several Variables

Parameterization and Vector Fields

Line Integrals

Flux Integrals and Divergence

The Curl and Stokes Theorem

Parameters, Coordinates, Integrals

Filters

Suppose a function is given by a table of values as follows: x 1.1 1.3 1.5 1.7 1.9 2.1 f(x) 14 17 23 25 26 27 Give your best estimate of $f^{\prime \prime}(1.9)$ .

Let $f(x)=x^{-2 / 3}$ .Use a graph to decide which one of the following statements is true.

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 17.00 meters per second and will attain a height of $s(t)=-0.8 t^{2}+17.00 t$ meters in t seconds.Find a formula for the velocity of the golf ball at time t.

For $f(x)=\log x$ , estimate f '(3)to 3 decimal places by finding the average slope over intervals containing the value x = 3.

A golf ball thrown directly upwards from the surface of the moon with an initial velocity of 14.00 meters per second and will attain a height of $s(t)=-0.8 t^{2}+14.00 t$ meters in t seconds.What is the acceleration of the golf ball at time t?

The graph below represents the rate of change of a function f with respect to x; i.e., it is a graph of f '.You are told that f (0)= 0.What can you say about $f(x)$ at the point x = 1.3? Mark all that apply.

Is the function $f(x)=\frac{x^{2}|2 x-4|}{x-2}$ continuous at x = 2?

To find the derivative of $g(x)=2 x^{2}+5 x-9$ at x = 8 algebraically, you evaluate the following expression.

Is the graph of $f(x)=|x+3|$ continuous at x = -3?