Understanding Derivatives and Their Implications

Understanding Derivatives and Their Implications

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

Anil Kumar explains the application of first derivatives to analyze a cubic function. The video covers finding the derivative, identifying turning points, and determining intervals of increase and decrease. It also discusses local maximum and minimum points and introduces a test points method for verification. The video concludes with an exercise to sketch the graph of the function.

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main focus of this video tutorial?

Solving quadratic equations

Integration techniques

Graph theory

Application of first derivatives

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the given function in the problem statement?

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

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

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

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

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the nature of the derivative of the given cubic function?

Constant

Quadratic

Linear

Cubic

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the function f(x) = 2x^3 - 3x + 4?

6x^2 - 3

3x^2 - 3

2x^2 - 3

3x^2 + 3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the quadratic derivative be factored?

3(x^2 + 1)

3(x + 1)(x - 1)

3(x^2 - 1)

3(x - 1)(x + 1)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the turning points of the function?

x = -1 and x = 1

x = 0 and x = 2

x = -2 and x = 2

x = 1 and x = 3

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a positive derivative indicate about the function?

The function is decreasing

The function has a maximum

The function is constant

The function is increasing

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