Answer:
Step-by-step explanation:
given a point the equation of a line with slope m that passes through the given point is
or equivalently
.
Recall that a line of the form , the y intercept is b and the x intercept is
.
So, in our case, the y intercept is and the x intercept is
.
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph . Which means that
The slope of the tangent line is given by the derivative of the function evaluated at . Using the properties of derivatives, we get
. So evaluated at
we get
Replacing the values in our previous findings we get that the y intercept is
The x intercept is
The triangle in consideration has height and base
. So the area is
So regardless of the point we take on the graph, the area of the triangle is always 2.