Question

What is the equation of the tangent line of `f(x) = 1/x` at `x = 2`?

Answer 1

4y + x - 4 = 0

Explanation:

To find the equation of the tangent y - b = m(x - a ) , require to find m and a point on the line (a , b ). To obtain m , differentiate f(x) and evaluate at x = 2 . To find (a , b ) evaluate f2)

`f(x) = 1/x = x^-1`

differentiate using the 'power rule'

f'(x)`= -x^-2 =- 1/x^2`

and f'(2)`= -1/2^2 =- 1/4 = m`

also f(2) =`1/2 rArr (a , b ) = ( 2 , 1/2 )`

equation of tangent : `y - 1/2 = -1/4(x - 2 )`

(multiply through by 4 to eliminate fractions )

hence : 4y - 2 = - x + 2

`rArr 4y + x - 4 = 0`