Question

What is the equation of the tangent line of `y=1/x` at `x=1`?

Answer 1

`y=-x+2` This the equation of tangent in slope-intercept form.

Explanation:

To find the equation of tangent line, first we need to find the slope of the tangent at x = 1.

`y=1/x`
`y= x^-1`
Differentiating with respect to x using `(d(x^n))/dx = n*x^(n-1)`

we get `dy/dx = -x^-2`
`dy/dx = -1/x^2`
`dy/dx at (x=1) = -1/(1)^2 = -1`

The slope of tangent "m" is -1

When `x=1` then `y=1/1 = 1`
We have a point (1,1) and a slope -1

Equation of tangent in slope point form is given by the formula

`y-y_1 =m(x-x_1)`
Here we have `m = -1`,`x_1 =1` and `y_1 = 1`
`y-1=-1(x-1)`
`y-1 = -x+1`

`y=-x+2` The final answer in slope intercept form.