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

1 Answer
Shwetank Mauria
Jun 16, 2016

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#

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