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posted by  freekina191 on 10/30/2009 11:10:19 PM  |  status: Closed  |  Earned Karma: 35

slope of tangent line? PLEASE HELP

Course Textbook Chapter Problem Needs by
Calculus Calculus (6th) by Stewart N/A N/A 10/30/2009 at 12:00:00 AM
Question Details:
1. Find the equation of the tangent line to the curve (a hyperbola)
\frac{x^2}{16} - \frac{y^2}{1} = 1
at the point ( -9 , \frac{1}{4}\sqrt{65} ). The equation of this tangent line can be written in the form y = mx+b where

m =

b =

2. Find the slope of the tangent line to the curve
\sqrt{4x +2y} + \sqrt{3xy} = 16.4
at the point ( 7,5 ).
Answer:
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posted by The Big Unit on 10/31/2009 12:10:52 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
1) You have the hyperbola
Solving for y as an explicit function of x yields:
 (due to the given point, you will want to use the negative solution)
So
Taking the derivative of  yields:
Evaluating the derivative at  yields:
Your equation of the line tangent to the given curve at the specified point will be:
So  and  (ANSWER 1)
2) You have the equation
Doing some simplification before taking the derivative implicitly, you will have:
Evaluating the derivative at the specified point yields:
 (ANSWER 2)
Jon AKA THE BIG UNIT
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