Find the equation of the normal line for f(x)= x+ (1/x) at the point x=2 in slope point form

Answer 1

The formula for equation of the normal line is

y-y1= -1 / f'(x1) [x-x1]

1. find the (x1,y1). The point x=2 is given. Plug x=2 into the given equation to get y.
2. When x1=2, y1=f(x)= 2+1/2= 5/2
3. Therefore, (x1,y1)= (2, 5/2).
4. find the f'(x). Derive the given equation of the line. f'(x)= 1- 1/(x^2)
5. Plug x=2. f'(x) = 1-1/4= 3/4
6. Put it all together in the normal line formula.
7. y-y1= -1 / f'(x1) [x-x1]

y- 5/2 = -1/ (3/4) [x-2]

y= -4/3 (x-2) +5/2