Cost Function Analysis and Derivatives

Cost Function Analysis and Derivatives

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

This video tutorial explains how to determine if a total cost function is concave or convex at specific points by using the second derivative. It demonstrates the process of finding the second derivative and evaluating it at different points to assess the nature of the cost function. The video also covers how to identify the inflection point where the cost function changes from concave to convex or vice versa. Key examples include analyzing the cost function at Q=2 for concavity and at Q=5 for convexity, as well as finding the inflection point at Q=3.

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9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main objective of the video?

To learn about cost functions in general

To determine concavity or convexity and find the inflection point of a cost function

To calculate the total cost of production

To understand the concept of marginal cost

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does it mean if a cost function is concave at a certain point?

The graph is undefined

The graph is linear

The tangent line lies above the graph

The tangent line lies below the graph

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first derivative of a cost function commonly known as?

Total cost

Fixed cost

Marginal cost

Average cost

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the second derivative of the cost function at Q equals 2?

24

0

12

-12

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a positive second derivative at a point indicate about the cost function?

The function is linear at that point

The function is undefined at that point

The function is concave at that point

The function is convex at that point

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the second derivative of the cost function at Q equals 5?

-12

0

24

36

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

At what value of Q does the inflection point occur?

Q equals 5

Q equals 4

Q equals 3

Q equals 2

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