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Chapter 2: Derivatives Test (From a Previous Year) Multiple Choice Circle the choice that best completes the statement or answers the question. Also write the letter corresponding to your choice on.

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The second derivative test uses the first and second derivative of a function to determine relative maximums and relative minimums of a function.

The positive second derivative at x tells us that the derivative of f(x) is increasing at that point and, graphically, that the curve of the graph is concave up at that point.

The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here.

The biggest difference is that the first derivative test always determines whether a function has a local maximum, a local minimum, or neither; however, the second derivative test fails to yield a conclusion when y'' is zero at a critical value.

Steps for Second Derivative Test Equalize the first derivative to zero f'(x) = 0 and find the limiting points x1,x2 x 1 , x 2 . Find the second derivative of the function f''(x). Substitute the limiting points in the second derivativef′′(x1),f′′(x2) f ″ ( x 1 ) , f ″ ( x 2 ) ..

The first derivative test fails when the points to the left and the right of the limiting point have the same derivative values. In this case, we cannot define if the limiting point is the maxima or the minima and this limiting point is called the point of inflection.

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© Copyright 1997-2025
airSlate Legal Forms, Inc.
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Form Packages
Adoption
Bankruptcy
Contractors
Divorce
Home Sales
Employment
Identity Theft
Incorporation
Landlord Tenant
Living Trust
Name Change
Personal Planning
Small Business
Wills & Estates
Packages A-Z
Form Categories
Affidavits
Bankruptcy
Bill of Sale
Corporate - LLC
Divorce
Employment
Identity Theft
Internet Technology
Landlord Tenant
Living Wills
Name Change
Power of Attorney
Real Estate
Small Estates
Wills
All Forms
Forms A-Z
Form Library
Customer Service
Terms of Service
Privacy Notice
Legal Hub
Content Takedown Policy
Bug Bounty Program
About Us
Blog
Affiliates
Contact Us
Delete My Account
Site Map
Industries
Forms in Spanish
Localized Forms
State-specific Forms
Forms Kit
Legal Guides
Real Estate Handbook
All Guides
Prepared for You
Notarize
Incorporation services
Our Customers
For Consumers
For Small Business
For Attorneys
Our Sites
US Legal Forms
USLegal
FormsPass
pdfFiller
signNow
airSlate WorkFlow
DocHub
Instapage
Social Media
Call us now toll free:
+1 833 426 79 33
As seen in:
  • USA Today logo picture
  • CBC News logo picture
  • LA Times logo picture
  • The Washington Post logo picture
  • AP logo picture
  • Forbes logo picture
© Copyright 1997-2025
airSlate Legal Forms, Inc.
3720 Flowood Dr, Flowood, Mississippi 39232