# Geometric derivative problem

1. Dec 31, 2011

### TheKracken

1. The problem statement, all variables and given/known data

we had a a function on a graph of f(x)=1/x and then we are suposed to find the area of a triangle where the tangent line is the hypontenuse, and the x and y axis are the base and hight.....i found f'(x)= -1/x^2
from here i used the formula y-yo=x0(x-x0) and got that the x intercept is 2xo and then got the y intercept to be 2yo which means those are the lengths of the base and the hight, from there you use the formula of a triangle and that is (2)(2)(xo)(yo) all over 2 and then i canceled out the 2's and got 2(xo)(yo) as the area of the triangle...and this all is correct...but how the heck does the also = 2??? apperantly 2(Xo)(Yo)=2....could someone please explain this, possibly just some basic algebra rule and i'm having a brain fart???

by the way, this is off of MIT's OCW.....

2. Dec 31, 2011

### SammyS

Staff Emeritus
What is y0 in terms of x0 ?

After all, isn't y0 = f(x0) ?

3. Jan 1, 2012

### TheKracken

yes....but I dont think that makes a difference....you still need some form of units dont you? because if the answer is 2...then its 2 what? 2 inches? 2 meters? I understood it all the way up untill he said therefor it =2

4. Jan 1, 2012

### SammyS

Staff Emeritus
The units will cancel.

The units of y are the reciprocal of the units of x.

The units of area for this graph are units of x times units of y.

5. Jan 1, 2012

### TheKracken

So I wouldnt be wrong if I left the units then would I? Or is it best to cancle and simplify like that?

Last edited: Jan 2, 2012
6. Jan 1, 2012

### SammyS

Staff Emeritus
The sentence doesn't make sense. Is there a typo ?

7. Jan 2, 2012

### TheKracken

sorry, yes there was some typos....fixed

8. Jan 2, 2012

### SammyS

Staff Emeritus
Whatever the units for x, the area of the triangle will not have units. It's a pure number.

9. Jan 2, 2012

### TheKracken

Alright...now that I am thinking about it I think I understand....its because the x's arnt labeled with a unit/number.