If I have f(x)=(x^2)/3x+2, what is an equation of the tangent line to f(x) at x=1?

Sorry about the delay, but I just managed to get on the PC and answer it.
I assume that is supposed to be f(x) = x^2/(3x+2).

Given that f(x) = g(x)/h(x), the quotient rule says that f'(x) = (hg' -gh')/h^2.

Since g(x) = x^2, g'(x) = 2x.
Since h(x) = 3x+2, h'(x) = 3.

That gives [(3x+2)2x - (x^2)3]/(3x+2)^2.
That works out to (6x^2 + 4x - 3x^2)/(3x+2)^2.
Combining terms and factoring out an x on top gives x(3x+4)/(3x+2)^2.

Sorry about that ... now to continue to answer.

The equation of a line at x=1 would be y = m(x-1) + b where
m was the slope of the line and b was the value of y at 1.

To find m, put 1 into the derivative.
To find the value for b, put 1 into the equation for f(x) and see what you get.  


All Answers

Answers by Expert:

Ask Experts




Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).


Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2017 All rights reserved.

[an error occurred while processing this directive]