Question 1

How can the tangent line of a function be found?

Accepted Answer

Derivatives

Answer

Integrals

Answer

Parabolas

Answer

Logarithms

Question 2

What are the main rules used in finding derivatives?

Accepted Answer

Product Rule, Quotient Rule, and Chain Rule

Answer

Implicit Differentiation, Point-Slope form, and Power Rule

Answer

Chain Rule, Power of a Power, and the Zero Product Property

Answer

Product Rule, Power Rule, and the Zero Product Property

Question 3

What is the derivative of f(x) = x³ + 2x⁴

Accepted Answer

f'(x) = 3x² + 8x³

Answer

f'(x) = x² + x⁴

Answer

f'(x) = x⁴ /4 + 2x⁵/5

Answer

f'(x) = 0

Question 4

What is the derivative of f(x) = e^x

Accepted Answer

f'(x) = e^x

Answer

f'(x) = 0

Answer

f'(x) = ln x

Answer

f'(x) = 0

Question 5

What is the derivative of f(x) = x

Accepted Answer

f'(x) = 1

Answer

f'(x) = x²

Answer

f'(x) = 2x

Answer

f'(x) = x

Question 6

What is the derivative of f(x) = x³ / 4

Accepted Answer

f'(x) = 3x²/4

Answer

f'(x) = 12x²/4

Answer

f'(x) = 3x²/16

Answer

f'(x) = 12x² / 16

Question 7

What is the derivative of f(x) = (x)²

Accepted Answer

f'(x) = 2x

Answer

f'(x) = 2x + 1

Answer

f'(x) = 3x

Answer

f'(x) = x²/2

Question 8

What is the derivative of f(x) = 3

Accepted Answer

f'(x) = 0

Answer

f'(x) = 3x³

Answer

f'(x) = 3y

Answer

f'(x) = 3x

Question 9

What is the derivative of f(x) = (5r - 6)³

Accepted Answer

f'(x) = 15(5r - 6)²

Answer

f'(x) = 3(5r-6)²

Answer

f'(x) = 5(r - 6)²

Answer

f'(x) = 2(5r-6)³

Question 10

What is the second derivative of f(x) = 3x²

Accepted Answer

f"(x) = 6

Answer

f"(x) = 6x

Answer

f"(x) = 3x

Answer

f'(x) = 6

Question 11

What is the derivative of f(x) = cos(x)

Accepted Answer

f'(x) = -sin(x)

Answer

f'(x) = sin(x)

Answer

f'(x) = cos(x) csc(x)

Answer

f'(x) = -cos(x)

Question 12

What is the second derivative of f(x) = cos(x)

Accepted Answer

f"(x) = -cos(x)

Answer

f"(x) = -sin(x)

Answer

f"(x) = cos(x) csc(x)

Answer

f"(x) = sin(x)

Question 13

What is the derivative of f(x) = (7x)(3x+4)

Accepted Answer

f'(x) = 42x + 28

Answer

f'(x) = 21x + 28

Answer

f'(x) = 28x + 21

Answer

f'(x) = 21x²+ 21x + 28

Question 14

What is the second derivative of f(x) = (7x)(3x+4)

Accepted Answer

f"(x) = 42

Answer

f"(x) = 21x²+ 21x + 28

Answer

f"(x) = 42x + 28

Answer

f"(x) = 21x + 28

Question 15

Which of the following is the Product Rule definition?

Accepted Answer

f(x) g'(x) + f'(x) g(x)

Answer

f(x) g'(x) - f'(x) g(x)

Answer

f(x) g'(x) - f'(x) g(x) /(g(x))²

Answer

f(x) g'(x) + f'(x) g(x) /(g(x))²

Question 16

Which of the following is the Quotient Rule definition?

Accepted Answer

f'(x) g(x) - f(x) g'(x) / (g(x))²

Answer

f(x) g'(x) - f'(x) g(x)

Answer

f'(x) g(x) + f(x) g'(x) / (g(x))²

Answer

f(x) g'(x) + f'(x) g(x)

Question 17

Which of the following derivatives requires the use of the Product Rule?

Accepted Answer

f(x) = (5x + 7)(3x³)

Answer

f(x) = (x⁴)/4

Answer

f(x) = (x + 3)⁵

Answer

f(x) = x²/4x

Question 18

Which of the following derivatives requires the use of the Chain Rule?

Accepted Answer

f(x) = (x⁸+ 9)⁹

Answer

f(x) = (9x)(86 + 7x⁴)

Answer

f(x) = (2x + 3) (4x)^-1

Answer

f(x) = (15x²) / (5)²

Question 19

What is the third derivative of f(x) = 2x⁵

Accepted Answer

f'''(x) = 120x²

Answer

f'''(x) = 10x⁴

Answer

f'''(x) = 15x⁵

Answer

f'''(x) = 40x³

Question 20

Who is modern differential calculus (derivatives) mostly accredited to?

Accepted Answer

Isaac Newton

Answer

Socrates

Answer

Albert Einstein

Answer

Aristotle

Question 21

Find dy/dx: y= x sinx

Accepted Answer

dy/dx = sinx - cosx

Answer

dy/dx = -sinx + cosx

Answer

dy/dx = sinx + cosx

Answer

dy/dx = -sinx - cosx

Question 22

Find the derivative of: f(x) = 1/x²

Accepted Answer

f'(x) = -2/x³

Answer

f'(x) = 2/x³

Answer

f'(x) = -2x³

Answer

f'(x) = 2x³

Question 23

What is the derivative of f(x) = 4 - 3x

Accepted Answer

f'(x) = -3

Answer

f'(x) = 4 - 3x²

Answer

f'(x) = 3

Answer

f'(x) = 3x

Question 24

What is the rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known?

Accepted Answer

Related Rates

Answer

Rate of Change

Answer

Rationalization

Answer

Implicit Differentiation

Question 25

What is the first step of solving a related rates problem?

Accepted Answer

Identify the formula that describes the relationship and any values that are constant

Answer

Read the formula

Answer

Differentiate with Respect to time

Answer

Identify and assign values to all variables within the derivative

Question 26

What is the first derivative of position?

Accepted Answer

Velocity

Answer

Speed

Answer

Friction

Answer

Acceleration

Question 27

What is the second derivative of position?

Accepted Answer

Acceleration

Answer

Friction

Answer

Speed

Answer

Velocity

Question 28

What is the absolute value of velocity?

Accepted Answer

Speed

Answer

Velocity

Answer

Acceleration

Answer

Friction

Question 29

In the first derivative test, if f'(x) changes from negative to positive at c, then f(c) is a __________ _________ of f.

Accepted Answer

Relative minimum

Answer

Concavity

Answer

Relative extrema

Answer

Relative maximum

Question 30

In the first derivative test, if f'(x) changes from positive to negative at c, then f(c) is a __________ _________ of f.

Accepted Answer

Relative maximum

Answer

Relative extrema

Answer

Relative minimum

Answer

Concavity

Question 31

Find dy/dx: x²+ y²= 64

Accepted Answer

dy/dx = -x/y

Answer

dy/dx = -2x / 2y

Answer

dy/dx = 2x + 2y

Answer

dy/dx = 2x - 2y

Question 32

What is the derivative of f(x) = x²+ 4x -5

Accepted Answer

f'(x) = 2x + 4

Answer

f'(x) = 2x + 4x + 5

Answer

f'(x) = -4 + 2x

Answer

f'(x) = 2x - 4

Question 33

What occurs where there is a change in concavity (f"(x) = 0)?

Accepted Answer

Points of Inflection

Answer

Critical Value Intersection

Answer

Second Derivative Test

Answer

Concavity Dip

Question 34

When testing for concavity, if f"(x) > 0 then the graph is __________ _________

Accepted Answer

Concave Upward

Answer

Right Shifted

Answer

Critically Shifted

Answer

Concave Downward

Question 35

When testing for concavity, if f"(x) < 0 then the graph is __________ _________

Accepted Answer

Concave Downward

Answer

Right Shifted

Answer

Critically Shifted

Answer

Concave Upward

Question 36

Concavity changes where the second derivative is equal to...

Accepted Answer

0

Answer

5

Answer

1

Answer

-1

Question 37

Let f be a function such that f'(c) = 0 and the second derivative exists on an open interval containing c. What is c?

Accepted Answer

Critical Values

Answer

Correlation

Answer

Concavity

Answer

Core Points

Question 38

What is the first step of finding open intervals where the function is increasing or decreasing?

Accepted Answer

Take the derivative

Answer

Review the Equation

Answer

Set the derivative equal to 0

Answer

Identify the constants

Question 39

How should you use the Power Rule when finding the derivative of a function?

Accepted Answer

Multiply the exponent by the coefficient and subtract 1 from the exponent

Answer

Divide the exponent by the coefficient and add 1 to the exponent

Answer

Multiply the exponent by the coefficient and add 1 to the exponent

Answer

Divide the exponent by the coefficient and subtract 1 from the exponent

Question 40

What must you add next to a y variable when finding the derivative of a function?

Accepted Answer

dy/dx

Answer

f'(x)

Answer

∫

Answer

dx/dy

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