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Understanding Concavity and Inflection Points with Differentiation

Instructions:

Choose an answer and hit 'next'. You will receive your score and answers at the end.

question 1 of 3

Consider the function f(x) below. At x = 1 is this function concave up, concave down, or an inflection point?

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1. Consider the function f(x) below. At x = 2 is this function concave up, concave down, or an inflection point?

2. Consider the function g(x) below. At x = 0 is this function concave up, concave down, or an inflection point?

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About This Quiz & Worksheet

Use this quiz to determine the concavity of functions. Consider the functions of each question and apply knowledge of the second derivative to determine each function's concavity.

Quiz & Worksheet Goals

In these assessments you'll be tested on the definitions of:

  • Concave up
  • Inflection point
  • Concave down

Skills Practiced

  • Problem solving - solve practice problems considering the concavity of functions
  • Distinguishing differences - compare and contrast topics from the lesson, such as concave up and concave down
  • Information recall - access the knowledge you've gained regarding concavity
  • Knowledge application - use your knowledge to answer questions about inflection points

Additional Learning

To learn more about concavity, review the accompanying lesson on Concavity and Inflection Points with Differentiation . This lesson covers the following objectives:

  • Determining the concavity of a function
  • Identifying when a function is both concave up and down
  • Understanding change of the second derivative from positive to negative
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