Consider f(x)=ax+xln(bx)f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x): f′(x)=f′(x)= ---------- Based on your expression for f′(x)f′(x), is f(x)f(x) increasing or decreasing? (Enter increasing or decreasing.) --------------- (Be sure that you can see why this is true for all values x>1x>1.) Find f′′(x)f″(x): f′′(x)=f″(x)= ---------- Based on your expression for f′′(x)f″(x), is f(x)f(x) concave up or concave down? (Enter up or down.)------------- (Be sure that you can see why this is true for all values x>1x>1.)

Consider f(x)=ax+xln(bx)f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x): f′(x)=f′(x)= ---------- Based on your expression for f′(x)f′(x), is f(x)f(x) increasing or decreasing? (Enter increasing or decreasing.) --------------- (Be sure that you can see why this is true for all values x>1x>1.) Find f′′(x)f″(x): f′′(x)=f″(x)= ---------- Based on your expression for f′′(x)f″(x), is f(x)f(x) concave up or concave down? (Enter up or down.)------------- (Be sure that you can see why this is true for all values x>1x>1.)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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