4.3 - 4.3 Connecting f and f with the Graph of f First...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Calculus Section 4.3 Page9 4.3 Connecting f and f with the Graph of f First Derivative Test for Local Extrema Theorem 4 First Derivative Test for Local Extrema The following test applies to a continuous function f x ( ) . At a critical point c : 1. If f changes sign from positive to negative at c 2. If f changes sign from negative to positive at c 3. If f does not changes sign from positive to negative at c At a left endpoint a : If f < 0 f > 0 ( ) for x > a At a right endpoint a : If f < 0 f > 0 ( ) for x > a Example 1 Using the First Derivative Text a) Find the critical points of f x ( ) = x 3 - 12 x - 5. Find the function’s local and absolute extreme values. Identify the intervals on which f is increasing and decreasing. Solve Analytically Verify Graphically
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Calculus Section 4.3 Page 10 b) Find the critical points of f x ( ) = x 2 - 3 ( ) e x . Find the function’s local and absolute extreme values. Identify the intervals on which
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at Saint Michael's College - Colchester, Vermont.

Page1 / 4

4.3 - 4.3 Connecting f and f with the Graph of f First...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online