Quiz about Flashcard Quiz Part 1

Question 1

Which function is pictured in the graph?

Accepted Answer

Graph of y = sin x

Answer

Graph of y = cos x

Answer

Graph of y = sec x

Answer

Graph of y = tan x

Question 2

Which function is pictured in the graph?

Accepted Answer

Graph of y = tan x

Answer

Graph of y = cos x

Answer

Graph of y = sec x

Answer

Graph of y = sin x

Question 3

Which function is pictured in the graph?

Accepted Answer

Graph of y = sec x

Answer

Graph of y = tan x

Answer

Graph of y = cos x

Answer

Graph of y = sin x

Question 4

Pick the equation graphed.

Accepted Answer

Graph of y = $$\frac{1}{x}$$

Answer

Graph of y = ln(x)

Answer

Graph of y = |x|

Answer

Graph of y = sqrt(x)

Answer

Graph of y = $$\sqrt{1-x^2}$$

Question 5

Pick the equation graphed.

Accepted Answer

Graph of y = $$\sqrt[]{x}$$

Answer

Graph of y = ln(x)

Answer

Graph of y = |x|

Answer

Graph of y = $$\frac{1}{x}$$

Answer

Graph of y = $$\sqrt{1-x^2}$$

Question 6

Pick the equation graphed.

Accepted Answer

Graph of y = $$\sqrt{1-x^2}$$

Answer

Graph of y = |x|

Answer

Graph of y = $$\frac{1}{x}$$

Answer

Graph of y = ln(x)

Answer

Graph of y = $$\sqrt[]{x}$$

Question 7

Pick the equation graphed.

Accepted Answer

Graph of y = ln(x)

Answer

Graph of y = |x|

Answer

Graph of y = $$\sqrt[]{x}$$

Answer

Graph of y = $$e^x$$

Answer

Graph of y = $$\sqrt{1-x^2}$$

Question 8

Pick the equation graphed.

Accepted Answer

Graph of y = $$e^x$$

Answer

Graph of y = |x|

Answer

Graph of y = $$\sqrt[]{x}$$

Answer

Graph of y = ln(x)

Answer

Graph of y = $$\sqrt{1-x^2}$$

Question 9

An even function is symmetric with respect to the ____

Accepted Answer

y-axis

Answer

x-axis

Answer

z-axis

Answer

origin

Question 10

An odd function is symmetric with respect to the ____

Accepted Answer

origin

Answer

y-axis

Answer

x-axis

Answer

z-axis

Question 11

Fill in the blank: The formula for the volume of a cone is _______.

Accepted Answer

V = $$(1/3)\pi r^2 h$$

Answer

$$V = \pi r^2 h$$

Answer

V = $$(4/3)\pi r^3$$

Answer

V = $$(1/2)\pi r^2 h$$

Question 12

Fill in the blank: The formula for the volume of a sphere is _______.

Accepted Answer

V = $$(4/3)\pi r^3$$

Answer

V = $$(1/3)\pi r^2 h$$

Answer

$$V = \pi r^2 h$$

Answer

$$V = 2\pi r^2$$

Question 13

Fill in the blank: The formula for the surface area of a sphere is _______.

Accepted Answer

$$A = 4\pi r^2$$

Answer

$$2\pi r^2$$

Answer

$$A = 4\pi r^3$$

Answer

A = $$\pi r^2$$

Question 14

Question 14.

Accepted Answer

1

Answer

0

Answer

DNE

Answer

$$\infty$$

Question 15

Question 15.

Accepted Answer

0

Answer

1

Answer

DNE

Answer

$$\infty$$

Question 16

The line through a point on a curve with slope equal to the slope of the curve at that point.

Accepted Answer

Tangent Line

Answer

Normal Line

Answer

Secant Line

Question 17

The line connecting two point on a curve.

Accepted Answer

Secant Line

Answer

Tangent Line

Answer

Normal Line

Question 18

The line perpendicular to the tangent line at the point of tangency.

Accepted Answer

Normal Line

Answer

Tangent Line

Answer

Secant Line

Question 19

f(x) is continuous at x = c when

II. $$\lim_{x\rightarrow c}f\left(x\right)$$ exists

I. $$f\left(c\right)$$ exists

III. $$\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)$$

Accepted Answer

All the above

Answer

I. and II.

Answer

II. and III.

Question 20

What does f'(x) tell you about a function?

Accepted Answer

All the above

Answer

slope of tangent line

Answer

instantaneous rate of change

Answer

slope of curve at a point

Question 21

Power rule for derivatives: $$\frac{d}{dx}(x^n) =$$ _______

Accepted Answer

$$nx^{n-1}$$

Answer

$$n x^{n}$$

Answer

$$x^{n-1}$$

Answer

$$n x^{n+1}$$

Question 22

Product rule for derivatives: $$\frac{d}{dx}(f(x)g(x)) =$$ _______

Accepted Answer

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

Answer

f(x)g(x)

Answer

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

Answer

f'(x)g'(x)

Question 23

Quotient rule for derivatives: $$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) =$$ _______

Accepted Answer

$$\frac{g(x)f$$

Answer

$$\frac{f(x)g$$

Answer

$$\frac{f$$

Answer

$$\frac{f$$

Question 24

Chain rule for derivatives: $$\frac{d}{dx}(f(g(x))) =$$ _______

Accepted Answer

$$f$$

Answer

$$f(g(x)) \cdot g$$

Question 25

Fill in the blank: The derivative of cos(x) with respect to x is _______.

Accepted Answer

-sin(x)

Answer

sin(x)

Answer

cos(x)

Answer

-cos(x)

Question 26

Fill in the blank: The derivative of sin(x) with respect to x is _______.

Accepted Answer

cos(x)

Answer

-sin(x)

Answer

sin(x)

Answer

-cos(x)

Question 27

Fill in the blank: The derivative of tan(x) with respect to x is _______.

Accepted Answer

$$sec^2(x)$$

Answer

sin(x)

Answer

tan(x)

Answer

$$cos^2(x)$$

Question 28

Fill in the blank: The derivative of cot(x) with respect to x is _______.

Accepted Answer

$$-csc^2(x)$$

Answer

$$sec^2(x)$$

Answer

tan(x)

Answer

$$csc^2(x)$$

Question 29

Fill in the blank: The derivative of sec(x) with respect to x is _______.

Accepted Answer

sec(x) tan(x)

Answer

sec(x) cot(x)

Answer

sec(x) sin(x)

Answer

sec(x) + tan(x)

Question 30

Fill in the blank: The derivative of csc(x) with respect to x is _______.

Accepted Answer

-csc(x) cot(x)

Answer

csc(x) tan(x)

Answer

sec(x) cot(x)

Answer

-sec(x) tan(x)

Question 31

Fill in the blank: The derivative of arcsin(x) with respect to x is _____.

Accepted Answer

$$\frac{1}{\sqrt{1 - x^2}}$$

Answer

$$\frac{1}{\sqrt{1 + x^2}}$$

Answer

$$arcsin(x) * sqrt(1 - x^2)$$

Answer

$$x / \sqrt{1 - x^2}$$

Question 32

Fill in the blank: The derivative of arccos(x) with respect to x is _____.

Accepted Answer

$$-1 / \sqrt{1 - x^2}$$

Answer

$$\frac{1}{\sqrt{1 - x^2}}$$

Answer

$$\frac{1}{1 + x^2}$$

Answer

$$-1 / (1 + x^2)$$

Question 33

Fill in the blank: The derivative of arctan(x) with respect to x is _____.

Accepted Answer

$$\frac{1}{1 + x^2}$$

Answer

$$\frac{1}{1 - x^2}$$

Answer

arctan(x)

Answer

$$2x / (1 + x^2)$$

Question 34

Fill in the blank: The derivative of arccot(x) with respect to x is _____.

Accepted Answer

$$-\frac{1}{1+x^2}$$

Answer

$$\frac{1}{1 + x^2}$$

Answer

$$2x / (1 + x^2)$$

Answer

arctan(x)

Question 35

Fill in the blank: The derivative of arcsec(x) with respect to x is _____

Accepted Answer

$$\frac{1}{(|x| \sqrt{x^2 - 1})}$$

Answer

$$\frac{x}{\sqrt{x^2 - 1}}$$

Answer

$$\frac{1}{x^2 + 1}$$

Answer

$$\frac{1}{\sqrt{1 - x^2}}$$

Question 36

The derivative of arccsc(x) with respect to x is

Accepted Answer

$$-\frac{1}{|x|\sqrt{x^2-1}}$$

Answer

$$\frac{1}{|x|\sqrt{x^2-1}}$$

Answer

$$-\frac{1}{x\sqrt{x^2+1}}$$

Answer

$$\frac{1}{x\sqrt{x^2-1}}$$

Question 37

Fill in the blank: Derivative of natural log: $$\frac{d}{dx} (\ln x) = \underline{\hspace{2cm}}$$

Accepted Answer

$$\frac{1}{x}$$

Answer

x

Answer

\ln x

Answer

$$e^x$$

Question 38

Fill in the blank: Derivative of log base $$a$$ : $$\frac{d}{dx} (\log_a x) = \underline{\hspace{2cm}}$$

Accepted Answer

$$\frac{1}{x \ln a}$$

Answer

$$\frac{1}{x a}$$

Answer

$$\ln a \cdot x$$

Answer

$$\frac{a}{x}$$

Question 39

Fill in the blank: Derivative of natural exponential function: $$\frac{d}{dx} (e^x) = \underline{\hspace{2cm}}$$

Accepted Answer

$$e^x$$

Answer

$$x e^x$$

Answer

$$x^e$$

Answer

$$e^{x+1}$$

Question 40

Fill in the blank: Derivative of exponential function of any base: $$\frac{d}{dx} (a^x) = \underline{\hspace{2cm}}$$

Accepted Answer

$$a^x \ln a$$

Answer

$$a^x \ln x$$

Answer

$$x^a \ln a$$

Answer

$$a^x$$

Question 41

Derivative of an inverse function: What is $$\frac{d}{dx} (f^{-1}(x)) =$$ ?

Accepted Answer

$$\frac{1}{f$$

Answer

$ f'(x) $

Answer

$$f^{-1}(x)$$

Question 42

If a function is differentiable at a point, then _________.

Accepted Answer

it must be continuous at that point. (Differentiability implies continuity.)

Answer

it must be discontinuous at that point.

Answer

it must be non-differentiable at that point.

Answer

it must have a jump at that point.

Question 43

List four ways in which a function can fail to be differentiable at a point.

Accepted Answer

Discontinuity, Corner, Cusp, Vertical tangent line

Answer

Oscillation, Periodicity, Symmetry, Translation

Answer

Continuous everywhere, Smooth curve, No inflection, Horizontal tangent

Answer

Constant function, Linear function, Quadratic function, Cubic function

Question 44

A critical number (also known as a critical point or critical value) of f(x) is _________.

Accepted Answer

a value of x in the domain of f at which either f'(x) = 0 or f'(x) does not exist.

Answer

a value of x where f(x) is always increasing.

Answer

a value of x where f(x) is undefined for all x.

Answer

a value of x where f''(x) = 0 always.

Question 45

If f'(x) > 0, then _________

Accepted Answer

f(x) is increasing.

Answer

f(x) is decreasing.

Answer

f(x) is constant.

Answer

f(x) has a maximum.

Question 46

If f'(x) < 0, then _________.

Accepted Answer

f(x) is decreasing.

Answer

f(x) is increasing.

Answer

f(x) is constant.

Answer

f(x) has a maximum.

Question 47

If f'(x) = 0, then _________.

Accepted Answer

f(x) has a horizontal tangent.

Answer

f(x) is always increasing.

Answer

f(x) has a vertical tangent.

Answer

f(x) is always decreasing.

Question 48

Definition: f(x) is concave up when _________.

Accepted Answer

f'(x) is increasing.

Answer

f'(x) is constant.

Answer

f(x) is decreasing.

Answer

f''(x) is negative.

Question 49

Definition: f(x) is concave down when _________.

Accepted Answer

f'(x) is decreasing.

Answer

f'(x) is constant.

Answer

f'(x) is increasing.

Answer

f(x) is linear.

Question 50

f''(x) > 0 means that f(x) is __________.

Accepted Answer

concave up (like a cup)

Answer

concave down (like a frown)

Answer

increasing everywhere

Answer

decreasing everywhere

Question 51

f''(x) < 0 means that f(x) is __________.

Accepted Answer

concave down (like a frown)

Answer

concave up (like a cup)

Answer

increasing everywhere

Answer

a linear function

Question 52

Definition: A point of inflection is a point on the curve where _________.

Accepted Answer

concavity changes.

Answer

the slope is always zero.

Answer

the function is undefined.

Answer

the curve has a maximum value.

Question 53

To find a point of inflection, _________.

Accepted Answer

look for where f'' changes signs, or, equivalently, where f' changes direction.

Answer

look for where f' is zero and f'' is positive.

Answer

look for where f is increasing and f' is negative.

Answer

look for where f'' is always positive.

Question 54

To find extreme values of a function, look for where _________.

Accepted Answer

the derivative is zero or undefined

Answer

the function is increasing

Answer

the second derivative is positive

Answer

the function is continuous

Question 55

By the First Derivative Test, when the derivative changes from positive to negative

Accepted Answer

there is a maximum

Answer

there is a minimum

Answer

there is a zero

Answer

the function is undefined

Question 56

By the First Derivative Test, when the derivative changes from negative to positive

Accepted Answer

there is a minimum

Answer

there is a maximum

Answer

there is a zero

Answer

the function is undefined

Question 57

The Second Derivative Test: If f'(x) = 0 and ________, then f has a maximum; if ________, then f has a minimum.

Accepted Answer

f''(x) < 0; f''(x) > 0

Answer

f''(x) > 0; f''(x) < 0

Answer

f''(x) = 0; f''(x) > 0

Answer

f''(x) > 0; f''(x) = 0

Question 58

Acceleration function a(t) = v'(t), the derivative of velocity, as well as ________, the second derivative of position.

Accepted Answer

s''(t)

Answer

s'(t)

Answer

v(t)

Answer

a'(t)

Question 59

A particle is moving to the left when ________.

Accepted Answer

v(t) < 0

Answer

v(t) > 0

Answer

a(t) < 0

Answer

s(t) > 0

Flashcard Quiz Part 1

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics