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Mr. Barone Calculus Exploration Name Period Group Exploration: Concavity and the 2nd Derivative Test for Local Extrema Section 5.3c Warmup: Extrema Poetry 1) Commit to memory: Concave up, shaped like.

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Working Definition. An inflection point is a point on the graph where the second derivative changes sign. In order for the second derivative to change signs, it must either be zero or be undefined. So to find the inflection points of a function we only need to check the points where f′′(x) is 0 or undefined.

The second derivative test states that if f(x) has a stationary point when x=c and if f″(c)=0 then the test is inconclusive and we should study the sign of the first derivative, f′(x), to classify the stationary point.

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

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.

The Second Derivative Test relates to the First Derivative Test in the following way. If f″(c)>0, then the graph is concave up at a critical point c and f′ itself is growing. Since f′(c)=0 and f′ is growing at c, then it must go from negative to positive at c.

The second derivative measures the instantaneous rate of change of the first derivative. The sign of the second derivative tells us whether the slope of the tangent line to is increasing or decreasing.

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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
DMCA Policy
About Us
Blog
Affiliates
Contact Us
Privacy Notice
Delete My Account
Site Map
All Forms
Search all Forms
Industries
Forms in Spanish
Localized Forms
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 workflows
DocHub
Instapage
Social Media
Call us now toll free:
1-877-389-0141
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