Question

How do you find the equation of the tangent line to the curve `f(x)= x + cos (x)` at x = 0?

Answer 1

Equation of tangent line is `x-y+1=0`

Explanation:

To find equation of tangent line of `f(x)=x+cosx` at `x=0`, we should first find the slope of the tangent and value of function at `x=0`. Then, we can get the equation of the tangent from point slope form of the equation.

At `x=0`, `f(x)=0+cos0=1`

Slope of tangent at `x=0` is given by value of `(dy)/(dx)` at `x=0`.

`(df)/(dx)=1-sinx`, the slope at `x=0` will be

`1-sin0=1-0=1`

Hence slope of tangent is `1`

Hence, equation of tangent line is

`(y-1)=1(x-0)` or `x-y+1=0`