Free Printable Integrals and Derivatives in Context

1.

If you're supposed to find the Average Value of $f\left(x\right)$ , then the units of the average value will be...

a)

the same as the unit for $f\left(x\right)$

b)

the units of the $\int_{ }f\left(x\right)$

c)

the units of the derivative of $f\left(x\right)$

2.

If you're supposed to find the average rate of change of $f\left(x\right)$ , then the units of the average value will be...

a)

the same as the unit for $f\left(x\right)$

b)

the units of the $\int_{ }f\left(x\right)$

c)

the units of the derivative of $f\left(x\right)$

3.

Average value is...

a)

$\frac{1}{b-a}\int_a^bf\left(x\right)dx$

b)

$\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$\int_a^bf\left(x\right)dx$

d)

$y-y_1=m\left(x-x_1\right)$

4.

Average rate of change is...

a)

$\frac{1}{b-a}\int_a^bf\left(x\right)dx$

b)

$\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$\int_a^bf\left(x\right)dx$

d)

$y-y_1=m\left(x-x_1\right)$

5.

$\int_{ }^{ }f'\left(2x\right)dx$

a)

$\frac{1}{2}f\left(2x\right)$

b)

$2f''\left(2x\right)$

c)

$2f\left(2x\right)$

d)

$\frac{1}{2}f''\left(2x\right)$

6.

$\int_{ }^{ }f'\left(\frac{1}{2}x\right)dx$

a)

$\frac{1}{2}f\left(\frac{1}{2}x\right)$

b)

$2f''\left(\frac{1}{2}x\right)$

c)

$2f\left(\frac{1}{2}x\right)$

d)

$\frac{1}{2}f''\left(\frac{1}{2}x\right)$

7.

If R(x) is an increasing function, then a Left Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

8.

If R(x) is a decreasing function, then a Left Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

9.

If R(x) is an increasing function, then a Right Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

10.

If R(x) is a decreasing function, then a Right Hand Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

11.

If R(x) is an increasing concave up function, then a Trapezoidal Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

12.

If R(x) is an increasing concave down function, then a Trapezoidal Riemann sum will be an...

a)

Underapproximation

b)

Overapproximation

13.

a)

b)

c)

d)

14.

a)

b)

c)

d)

15.

What does this picture represent?

a)

Left Riemann Sum

b)

Right Riemann Sum

c)

Middle Riemann Sum

d)

Trapezoidal Sum

16.

The area under a curve is calculated using which mathematical concept?

a)

antiderivative

b)

indefinite integral

c)

definite integral

d)

derivative

17.

The fundamental theorem of calculus is basically:

a)

calculating the area under a curve

b)

$\int_a^b\ f\left(x\right)\ dx=F\left(b\right)-F\left(a\right)$

c)

integrating a function, with no +C

d)

using rectangles to approximate the area under a curve

e)

we didn't learn this!

18.

In the following picture, what does the

+

mean about the graph of

f\left(x\right)

a)

$f\left(x\right)$ is increasing

b)

$f\left(x\right)$ is decreasing

c)

$f\left(x\right)$ is positive

d)

$f\left(x\right)$ is negative

19.

In the following picture, what does the

-

mean about the graph of

f\left(x\right)

a)

$f\left(x\right)$ is increasing

b)

$f\left(x\right)$ is decreasing

c)

$f\left(x\right)$ is positive

d)

$f\left(x\right)$ is negative

20.

Consider the $f'\left(x\right)$ sign chart. What can you conclude about the point $x=2$ on $f\left(x\right)$ ?

a)

local maximum

b)

local minimum

c)

stationary point/platuae point

21.

Consider the $f'\left(x\right)$ sign chart. What can you conclude about the point $x=6$ on $f\left(x\right)$ ?

a)

local maximum

b)

local minimum

c)

stationary point/platuae point

22.

Consider the $f'\left(x\right)$ sign chart. What can you conclude about the point $x=9$ on $f\left(x\right)$ ?

a)

local maximum

b)

local minimum

c)

stationary point/platuae point

23.

Consider the $f'\left(x\right)$ sign chart. What is $f'\left(3\right)=$ ?

a)

$0$

b)

$+$

c)

$-$

d)

unknown

24.

When $f'\left(x\right)$ changes from positive to negative, this is called a

a)

local maximum

b)

local minimum

c)

stationary point

25.

When $f'\left(x\right)$ changes from negative to positive, this is called a

a)

local maximum

b)

local minimum

c)

stationary point

26.

When making a sign chart from a graph of

f\left(x\right)

, you can identify the critical points by identifying

a)

local maximums, minimums, and plateau points

b)

zeros on the graph (x intercepts)

c)

intervals when the graph is above the x axis

d)

intervals when the graph is increasing

27.

When making a sign chart from a graph of

f'\left(x\right)

,the derivative of

f\left(x\right)

, you can identify the critical points by identifying

a)

local maximums, minimums, and plateau points

b)

zeros on the graph (x intercepts)

c)

intervals when the graph is above the x axis

d)

intervals when the graph is increasing

28.

When making a sign chart from a graph of

f\left(x\right)

, you can identify the regions marked positive, +, by identifying

a)

intervals when the graph is below the x axis

b)

intervals when the graph is decreasing

c)

intervals when the graph is above the x axis

d)

intervals when the graph is increasing

29.

When making a sign chart from a graph of

f\left(x\right)

, you can identify the regions marked negative, -, by identifying

a)

intervals when the graph is below the x axis

b)

intervals when the graph is decreasing

c)

intervals when the graph is above the x axis

d)

intervals when the graph is increasing

30.

When making a sign chart from a graph of

f'\left(x\right)

, the derivative of

f\left(x\right)

, you can identify the regions marked negative, -, by identifying

a)

intervals when the graph is below the x axis

b)

intervals when the graph is decreasing

c)

intervals when the graph is above the x axis

d)

intervals when the graph is increasing

31.

When making a sign chart from a graph of

f'\left(x\right)

, the derivative of

f\left(x\right)

, you can identify the regions marked positive, + , by identifying

a)

intervals when the graph is below the x axis

b)

intervals when the graph is decreasing

c)

intervals when the graph is above the x axis

d)

intervals when the graph is increasing

Integrals and Derivatives in Context

Total questions: 31

Worksheet time: 16mins

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