Calc Question: Tangent Lines

1. Oct 24, 2005

joshb110

I'm royally confused... dont even know where to start..

Find the point(s) on the graph of y = 1/x where the tangent line is parallel to 4x + 9y = 3. The m of 4x + 9y = 3 is -4/9 and sadly, thats all i know...

2. Oct 24, 2005

joshb110

3. Oct 24, 2005

amcavoy

First of all, what is the derivative of 1/x. Do you know how to calculate this? Remember that the derivative at some point x0 is the slope of the graph at that point.

4. Oct 24, 2005

joshb110

hi. the derivative of 1/x = -1/ x^2, i believe.

5. Oct 24, 2005

joshb110

what do i do next? do i just graph the two equations?

6. Oct 24, 2005

HallsofIvy

Staff Emeritus
You mean as opposed to actually answering the question??

The problem, as you posted it, "Find the point(s) on the graph of y = 1/x where the tangent line is parallel to 4x + 9y = 3."

You know that the slope of 4x+ 9y= 3 is -4/9, you know that the derivative of y= 1/x at any x is y'= -1/x2 and you know, because apmcavoy just told you, that the derivative at a point is the slope of the tangent line there. For what x is the derivative equal to -4/9?