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

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Answer 1 · 2016-10-05T16:05:53

$y = x + 1$ $y=x+1$

First, find the derivative of the equation

$f' (x) = 1 - sin x$ $f'(x)=1-sinx$

Input $x$ $x$ to find the value of the slope

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

Simplify

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

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

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

$1 = (1) (0) + b$ $1=(1)(0)+b$

Solve for $b$ $b$ . Simplify

$1 = b$ $1=b$

Write the equation of the tangent line.

$y = 1 x + 1$ $y=1x+1$

$or$ $or$

$y = x + 1$ $y=x+1$

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