School

University of OttawaDepartment

MathematicsCourse Code

MAT 1300Professor

Termeh KoushaStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**18 pages of the document.**Curve Sketching

MAT 1300 A & D

Fall, 2016

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

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+ 16x3−30x2−9.

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

1 THE SECOND-DERIVATIVE TEST 3

Ex: Use the second derivative test to ﬁnd and classify the critical points for

f(x) = (x2−8x+ 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.

###### You're Reading a Preview

Unlock to view full version