You are here:

Calculus/finding the equation of the tangent line

Advertisement

Expert: - 6/27/2008


Question
My problem is:
The point P(5,2) lies on the curve y=sqrt(x-1).  Find an equation of the tangent line to the curve at P(5,2).  

I've been taught to solve this by finding the slope of the secant line, however, I'm really unsure of how to go about doing this.  

So far, I've graphed the equation and found a second point Q(10,3) and the slope of the line between those to points.  So, mPQ = 5.  I'm really not sure where to go from here though or even if I'm going in the right direction.  

Thanks for your help!  

Answer
I'm not sure if that's the right direction or not.  Here is what I do know.

To find a tangent line, we have a point and we know that it is parallel to the curve at (5,2).  Note that x^0.5 is the same as x^(1/2).  The slope of the line is the dervative at this point.  Since the function is (x-1)^0.5, the derivative is 0.5(x-1)^-0.5 = 1/(2(x-1)^0.5).  Put in the x value to find the slope and use (5,2) as (x0,y0).  That all fits into the point-slope form of a line.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

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.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. 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.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
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 junior level courses my sophomore year.

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.

©2012 About.com, a part of The New York Times Company. All rights reserved.