Show that every triangle formed by the enclosure of axes and a tangent of f(x) = 1/x has an area of 2.

Without using calculus

Question

Show that every triangle formed by the enclosure of axes and a tangent of f(x) = 1/x has an area of 2.

Without using calculus

agent0smith · Answer

I don't think you'd want calculus for this anyway.

Explain this "a tangent of f(x) = 1/x"

agent0smith · Answer

The hypotenuse of the triangle is tangent to 1/x?

ganeshie8 · Answer

Exactly...

ganeshie8 · Answer

Oh take only the curve in first quadrant

ganeshie8 · Answer

that tangent part requires calculus 
But I'm hoping we can avoid calculus here if we can somehow tale advantage of the symmetry over line y=x

agent0smith · Answer

That's what i was thinking... the tangent needs calc

You have the point of tangency on the curve/hypotenuse as (x, 1/x)

I'll come back to this later.

myininaya · Answer

@ganeshie8 can you draw an example of one triangle with the mentioned conditions 
I'm having trouble understanding

ganeshie8 · Answer

Okay just a sec

satellite73 · Answer

it seems to me to come down to finding the x coordinate on y = 0
not sure how to do this without the slope though 
is there a trick?

ganeshie8 · Answer

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