Search Header Logo
Graphing Functions and Their Derivatives

Graphing Functions and Their Derivatives

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

The video tutorial explains the concept of derivatives, focusing on graphing first and second derivatives. It illustrates how derivatives relate to the original function, using examples like a parabola and a ball's motion. The tutorial covers key concepts such as rate of change, concavity, and inflection points. It concludes with an example of graphing a cubic function using derivatives, emphasizing the importance of understanding derivatives for both math and physics.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary concept that helps us graph the derivatives of functions?

The derivative of a function is always negative.

The derivative of a function is always positive.

The value of a function and its rate of change are unrelated.

The value of a function and its rate of change are related.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When graphing the derivative of a parabola that opens downwards, what happens at the vertex?

The derivative is undefined.

The derivative is at its minimum.

The derivative is zero.

The derivative is at its maximum.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the context of a ball being tossed, what does the second derivative represent?

The position of the ball.

The velocity of the ball.

The acceleration of the ball.

The time of flight.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a positive second derivative indicate about a function's concavity?

The function is concave up.

The function has a local minimum.

The function has a local maximum.

The function is concave down.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is an inflection point in the context of a function's graph?

A point where the function has a local maximum.

A point where the function has a local minimum.

A point where the function is undefined.

A point where the function changes concavity.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first derivative of the function x^3 - 12x + 1?

6x

3x^2 - 12

x^2 - 12

3x^2 + 12

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find the local maxima and minima of a function using its first derivative?

By finding where the first derivative is undefined.

By finding where the first derivative is zero.

By finding where the first derivative is negative.

By finding where the first derivative is positive.

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?