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.
The Attempt at a Solution
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_)
where Base = |b| = 3/4
where height = |x| = 3
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