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Final

MAT 1300 Lecture 1: Curve sketchingExam


Department
Mathematics
Course Code
MAT 1300
Professor
Termeh Kousha
Study Guide
Final

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Curve Sketching
MAT 1300 A & D
Fall, 2016

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1 THE SECOND-DERIVATIVE TEST 2
1 The Second-derivative Test
The Second-derivative Test: Let x=abe a critical number of a function
f(x) such that f(a) = 0.
1. If f′′(a)<0 then x=ais a relative maximum of f(x).
2. If f′′(a)>0 then x=ais a relative minimum of f(x).
Ex: Find and classify all the relative extrema of
f(x) = 3x4+ 16x330x29.

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1 THE SECOND-DERIVATIVE TEST 3
Ex: Use the second derivative test to find and classify the critical points for
f(x) = (x28x+ 16)ex.
Note that just because f′′ (c) = 0 does not mean cis an inflection point.
Ex: show that f(x) = x4has a point cwhere the second derivative is zero
but x=cis not an inflection point.
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