This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: troyer (lmt836) Section 4.3 isaacson (55826) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points The derivative of a function f is given for all x by f ( x ) = (3 x 2- 3 x- 18) parenleftBig 1 + g ( x ) 2 parenrightBig where g is some unspecified function. At which point(s) will f have a local maximum? 1. local maximum at x =- 3 2. local maximum at x = 2 3. local maximum at x = 3 4. local maximum at x =- 2 , 3 5. local maximum at x =- 2 correct Explanation: At a local maximum of f , the derivative f ( x ) will be zero, i.e. , 3( x- 3)( x + 2) parenleftBig 1 + g ( x ) 2 parenrightBig = 0 . Thus the critical points of f occur only at x =- 2 , 3. To classify these critical points we use the First Derivative test; this means looking at the sign of f ( x ). But we know that 1 + g ( x ) 2 is positive for all x , so we have only to look at the sign of the product 3( x- 3)( x + 2) of the other two factors in f ( x ). Now the sign chart- 2 3 + +- for 3( x- 3)( x + 2) shows that the graph of f is increasing on (- ,- 2), decreasing on (- 2 , 3), and increasing on (3 , ). Thus f has a local maximum at x =- 2 . 002 10.0 points Use the graph a b c of the derivative of f to locate the critical points x at which f has a local maximum?...
View Full Document
This note was uploaded on 06/14/2011 for the course MATH 305G taught by Professor Cathy during the Spring '11 term at University of Texas at Austin.
- Spring '11