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## Homework Statement

the tangent of the graph 1/x^2 at P(2,1/4) forms a triangle with the x and y axis. Find area of triangle.

## Homework Equations

## The Attempt at a Solution

so f'(x)=-2/x^3

so the slope of the tangent at point 2, is f'(2)=-2/8 = -1/4=mt

now i use the equation of the line to determine x + y intercepts

y=mtx+b plug in point P(2,1/4)

1/4=-1/4(2) + b

b=3/4 (y intercept_)

y=-1/4x+3/4

let y=0

0=-1/4x+3/4

x=3

therefore AreaΔ=bxh/2

where Base = |b| = 3/4

where height = |x| = 3

A=(3/4)(3)/2

A=9/8 units^2

I beleive this is the correct solution, to me everything makes sense, but i'm just kind of nervous about the area.. 9/8 units i mean i know its possible but i dunno... I'm worried i'm messing my numbers up or something.

***i found a mistake where my slope was 1/4 and it was supposed to be -1/4

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