Question

Find an equation of the line that is perpendicular to the tangent to the graph of f(x)=1/x at x=2 and that intersects it at the point of tangency.

Answer 1

y = 1/x
dy/dx = -1/x^2
at x= 2, y = 1/2
at x = 2, dy/dx = -1/4
now slope of the line which is perpendicular to the tangent will be
(-1/4)*m = -1
=> m = 4

Answer 2

from the first dy/dx why did the x turn to x^2 and the 1 to a -1?

Answer 3

so the equation of the line perpendicular to the tangent and passing through the point of tangency (2,1/2) will be:
(y-1/2) = 4 (x-4)

Answer 4

differentiation of 1/x with respect to x is -1/x^2.

Answer 5

dy/dx is nothing but the slope of the tangent at that particular curve.

Answer 6

Im so sorry, but what is differentiation again? I forgot this