Question

its a Q from chapter 2
Q) The tangent to the graph of f(x)=2/x at the point (1,2) forms a triangle with the x and y axes. find the perimeter of the triangle, in units. do not simplify your answer.

Answer 1

dy/dx = -2/x^2
at pt. (1,2)
dy/dx = -2

So slope of tangent = -2
Equation of tangent : y - 2 = -2(x-1)
which is 2x + y = 4



Length of hypotenuse is sqrt20

So perimeter = 6+ sqrt20 units