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.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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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.)
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