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

Oct 5, 2016

$y = x + 1$

Explanation:

First, find the derivative of the equation

$f ' \left(x\right) = 1 - \sin x$

Input $x$ to find the value of the slope

$f ' \left(0\right) = 1 - \sin \left(0\right)$

Simplify

$f ' \left(0\right) = 1 - 0 = 1$

The slope, $m$, is $1$.

Make the substitutions into the slope intercept formula, $y = m x + b$

$1 = \left(1\right) \left(0\right) + b$

Solve for $b$. Simplify

$1 = b$

Write the equation of the tangent line.

$y = 1 x + 1$

$\mathmr{and}$

$y = x + 1$

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