Critical Points and Derivatives

Critical Points and Derivatives

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial by Amal Kumar explains how to find and analyze critical points of functions using the first derivative test. It covers the process of finding derivatives, identifying critical points, and using test points to determine if these points are local maxima, minima, or neither. The tutorial includes two examples, demonstrating the method with different functions.

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8 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding critical points of a function?

Find the derivative of the function

Graph the function

Find the second derivative

Set the function equal to zero

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it useful to factor the derivative of a function?

To determine the function's range

To simplify the function

To calculate the second derivative

To find the critical points more easily

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When is a critical point found?

When the function is increasing

When the derivative is positive

When the derivative is zero or undefined

When the function is decreasing

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a negative derivative indicate about the function's graph?

The graph is decreasing

The graph is constant

The graph is increasing

The graph is undefined

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a change from a negative to a positive derivative indicate?

A local maximum

A local minimum

A point of inflection

A constant function

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the function G(x) = 3x^4 - 4x^3?

12x^4 - 4x^3

3x^3 - 4x^2

3x^4 - 4x^3

12x^3 - 12x^2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the critical points of the function G(x) = 3x^4 - 4x^3?

x = -1 and x = 0

x = 1 and x = 2

x = 2 and x = 3

x = 0 and x = 1

8.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does it mean if the derivative is negative on both sides of a critical point?

The point is a local maximum

The point is a local minimum

The function is constant

The point is neither a maximum nor a minimum