How do you find the equation of the tangent line to the curve #y= x + cos x# at (0,1)?

Question

24564 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-05T16:05:53

#y=x+1#

First, find the derivative of the equation

#f'(x)=1-sinx#

Input #x# to find the value of the slope

#f'(0)=1-sin(0)#

Simplify

#f'(0)=1-0=1#

The slope, #m#, is #1#.

Make the substitutions into the slope intercept formula, #y=mx+b#

#1=(1)(0)+b#

Solve for #b#. Simplify

#1=b#

Write the equation of the tangent line.

#y=1x+1#

#or#

#y=x+1#

Check out the following tutorials for more examples.