## f(5)=1/10## is a local max.## f(-5)=-1/10## is a local min.
##f(x)={x}/{x^2+25}##
By ,
##f'(x)={1 cdot(x^2+25)-x cdot 2x}/{(x^2+25)^2}={25-x^2}/{(x^2+25)^2}=0##
##=> x= pm5″ “## (Critical Numbers)
First Derivative Test
##{(f’:(-) to (+)” at “x=-5 => f(-5)=-1/10″ is a local min.”),(f’:(+) to (-)” at “x=5 => f(5)=1/10″ is a local max.”):}##
Second Derivative Test
By Quotient Rule,
##f”(x)={ -2x(x^2+25)^2-(25-x^2)cdot2(x^2+25)(2x)}/{(x^2+25)^4}={2x(x^2-75)}/(x^2+25)^3##
##{(f”(-5)>0 => f(-5)=-1/10″ is a local min.”),(f”(5)<0 => f(5)=1/10″ is a local max.”):}##
I hope that this was helpful.
“Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!”
What Students Are Saying About Us
.......... Customer ID: 12*** | Rating: ⭐⭐⭐⭐⭐"Honestly, I was afraid to send my paper to you, but splendidwritings.com proved they are a trustworthy service. My essay was done in less than a day, and I received a brilliant piece. I didn’t even believe it was my essay at first 🙂 Great job, thank you!"
.......... Customer ID: 14***| Rating: ⭐⭐⭐⭐⭐
"The company has some nice prices and good content. I ordered a term paper here and got a very good one. I'll keep ordering from this website."
