Free Printable quiz 1050

1.

Over what interval is this function constant?

a)

-5 < x < ∞

b)

-3 < x < 4

c)

4 < x < ∞

d)

-5

2.

When is this function increasing?

a)

-2.5 < x < 2.5

b)

0 < x < 5

c)

0 < x < 55

d)

-5 < x < 0

3.

What is the increasing interval for the function below?

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,2\right]$

c)

$\left(-\infty,6\right]$

d)

$\left(-6,6\right)$

4.

What is/are the increasing interval(s) for the function shown?

a)

$\left(-3,\ 1\right)$

b)

$\left(4,\ 8\right)$

c)

$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

5.

What is the increasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

6.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

7.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

$\left(-3,\ \infty\right)$

8.

What is the increasing interval on the function shown?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

$\left(-3,\ \infty\right)$

9.

What is the increasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\ and\ \left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\ and\ \left(2,\ \infty\right)$

10.

Choose all intervals where the graph is DECREASING (Choose all that apply)

a)

(-∞ , 1)

b)

(1 , 3)

c)

(3 , ∞)

11.

Choose all intervals where the graph is Increasing (Choose all that apply)

a)

(-∞ , 1)

b)

(1 , 3)

c)

(3 , ∞)

12.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

13.

Where is the function Increasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

14.

When is this function increasing?

a)

(-3, 3)

b)

(-2.5, 2.5)

c)

[-3, 3]

d)

(3, ∞)

15.

When is this function decreasing?

a)

(-3, 3)

b)

(-2.5, 2.5)

c)

[-3, 3]

d)

(3, ∞)

e)

$\left(-\infty,-3\right)\cup\left(3,\infty\right)$

16.

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

a)

There is a local max at x=3

b)

There is a local min at x = 3

c)

There is an inflection point at x = 3

d)

There is an x-intercept at x = 3

17.

The function $f(x)=x^3\ –\ 6x^2+9x+15$ is local maxima at

a)

x = 1

b)

x = 3

c)

no point of maxima and minima

d)

none of these

18.

The function $f(x)=x^3\ –\ 3x+3$ is

a)

local maximum at x = - 1

b)

local minimum at x = - 1

c)

local maximum at x = 1

d)

none of these

19.

Differentiate y= x³ + 2x

a)

3x³+2x

b)

3x²+2

c)

3x+2

d)

3x

20.

What is the derivative of a constant, C?

a)

C

b)

1

c)

0

21.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

22.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

23.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

24.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

25.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

26.

What are the decreasing intervals?

a)

All real numbers

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,2\right)\cup\left(3.25,\ \infty\right)$

c)

$\left(2,\ 3.25\right)$

d)

$\left(2,\ \infty\right)$

27.

What are the increasing intervals?

a)

All real numbers

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,2\right)\cup\left(3.25,\ \infty\right)$

c)

$\left(2,\ 3.25\right)$

d)

$\left(2,\ \infty\right)$

28.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

29.

For the pictured polynomial, which of the following are a relative min?

a)

(3, -2)

b)

(0, 3)

c)

(2, 0)

d)

(4, 1)

e)

(-3,-2)

30.

For the pictured polynomial, which can be a relative max?

a)

(-3, -2)

b)

(0, 3)

c)

(2, 0)

d)

(4, 1)

e)

(-5,1)

31.

There is a relative maximum at:

a)

x = -1

b)

x = 3

c)

x = -0.5

d)

x = 1.5

32.

What is the extrema for this function?

a)

Max; (-2,-1)

b)

Min; (-2,-1)

c)

Max; (-2,1)

d)

Min; (-2,1)

33.

What is the extrema for this function?

a)

Max; (-1,4)

b)

Min; (-1,4)

c)

Max; (0,3)

d)

Min; (0,3)

34.

Find the local maximum and minimum

a)

Local max at x = -3

Local min at x = -3

b)

Local max at x = 1

Local min at x = -3

c)

Local max at x = -3

Local min at x = 1

d)

$\left(-\infty,\ \infty\right)$

35.

Identify the local minimum

a)

x = 8

b)

x = 4

c)

$\infty$

d)

x = 2

36.

What is the relative max?

a)

x = 0

b)

x = -2.55

c)

(-∞, ∞)

d)

None

37.

What is the increasing interval for the function below?

a)

$\left(-\infty,\infty\right)$

b)

$\left(-\infty,2\right]$

c)

$\left(-\infty,6\right]$

d)

$\left(-6,6\right)$

38.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

$\left(-3,\ \infty\right)$

39.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

40.

Identify the interval from the derivative graph where the function is concave up.

a)

(-1,1) & (3,4)

b)

(-3,-2)

c)

(-2,-1)

d)

(-3,-1) & (1,3)

41.

Identify the interval from the derivative graph where the function is concave down

a)

(-1,1) & (3,4)

b)

(-2,4)

c)

(-3,-1) & (1,3)

d)

(-2,1) & (1,4)

42.

When f'(x) changes from negative to positive, there is(are) ...

a)

a maximum.

b)

a minimum.

c)

no extrema.

d)

an inflection point.

43.

When f'(x) changes from positive to negative, there is(are) ...

a)

a maximum.

b)

a minimum.

c)

no extrema.

d)

an inflection point.

44.

What will be true at an inflection point? (select the best answer)

a)

f(x)=0

b)

f'(x)=0

c)

f''(x)=0

d)

The function is undefined

45.

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

46.

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

a)

an inflection point

b)

a critical point

c)

a relative maximum

d)

a relative minimum

47.

The slope of a function is described by its ____________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

48.

Determine the derivative of: f(x) = x⁴sinx

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

49.

If f(x) = sin³(2x), then f'(x) =

a)

3cos(2x)

b)

3sin(2x)⋅2

c)

3sin²(2x)cos(2x)

d)

3sin²(2x)cos(2x)⋅2

50.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

51.

What is the derivative of tan(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

52.

y= sin²x find y'

a)

2sin x

b)

2(sin x)(cos x)

c)

2cos x

d)

2x(cos x)

53.

$\frac{d}{dx}\left(\cos x\right)=$

a)

$\sin x$

b)

$\sec x$

c)

$-\sin x$

d)

$-\sec x$

54.

$\frac{d}{dx}\left(\tan x\right)=$

a)

$\sec x\tan x$

b)

$\sec^2x$

c)

$-\csc x\cot x$

d)

$-\csc^2x$

55.

$\frac{d}{dx}\left(\csc x\right)=$

a)

$\sec x\tan x$

b)

$\sec^2x$

c)

$-\csc x\cot x$

d)

$-\csc^2x$

56.

$\frac{d}{dx}\left(x-3\sin x\right)=$

a)

$1-3\cos x$

b)

$1+3\cos x$

c)

$1-3\sin x$

d)

$1+3\sin x$

57.

$\frac{d}{dx}\left(x\sin x\right)=$

a)

$\cos x$

b)

$x\sin x+\cos x$

c)

$x\cos x+\sin x$

d)

$x\sin x-\cos x$

58.

$\frac{d}{dx}\left(\sin x+\cos x\right)=$

a)

$\sin x+\cos x$

b)

$\sin x-\cos x$

c)

$-\sin x+\cos x$

d)

$-\sin x-\cos x$

59.

$\frac{d}{dt}\left(4\sec t+\tan t\right)=$

a)

$4\tan t+\sec t$

b)

$4\sec t+\tan t$

c)

$\tan t\left(4\sec t+\tan t\right)$

d)

$\sec t\left(4\tan t+\sec t\right)$

60.

$\frac{d}{dt}\left(4\sec t+\tan t\right)=$

a)

$4\tan t+\sec t$

b)

$4\sec t+\tan t$

c)

$\tan t\left(4\sec t+\tan t\right)$

d)

$\sec t\left(4\tan t+\sec t\right)$

61.

$\frac{d}{dx}\left(\frac{\sin x}{x^2}\right)=$

a)

$\frac{\cos x}{2x}$

b)

$\frac{x\cos x-2\sin x}{x^3}$

c)

$\frac{2\cos x-x\sin x}{x^3}$

d)

$\frac{x^2\cos x+2\sin x}{x^4}$

62.

Please select the correct solution

a)

csc x

b)

sec x

c)

cot x

d)

tan x

63.

Find y' if

y = 10sin(x) +3cos(x)

a)

10sin(x)cos(x)+ 3cos(x)sin(x)

b)

10cos(x) - 3cos(x)

c)

30cos(x)sin(x)

d)

10cos(x) -3sin(x)

64.

$\frac{d}{dx}\left(x\sin x\right)=$

a)

$\cos x$

b)

$x\sin x+\cos x$

c)

$x\cos x+\sin x$

d)

$x\sin x-\cos x$

quiz 1050

Total questions: 64

Worksheet time: 2hrs 54mins

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