Question

Determine the equation of the tangent to f(x)= (1/x)+x at the point (1,2)

Answer 1

f' = -1/x^2 + 1 = (x^2-1)/x^2
f'(1) = 0

so, using the point-slope form,

y-2 = 0(x-1)
or,
y=2

http://www.wolframalpha.com/input/?i=plot+y%3D1%2Fx+%2B+x,+y%3D2,+0+%3C%3D+x+%3C%3D+2