How do you find the equation of the tangent line to the curve $f (x) = \frac{x + 1}{x + 2}$ $f(x)= (x+1)/(x+2)$ at x=0?

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How do you find the equation of the tangent line to the curve $f (x) = \frac{x + 1}{x + 2}$ $f(x)= (x+1)/(x+2)$ at x=0?

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Answer 1 · 2016-12-30T07:07:36

$y = \frac{1}{4} x + \frac{1}{2}$ $y = 1/4x + 1/2$

Explanation:

1) Find the first derivative of f(x).
2) Plug x = 0 into f '(x) to find the slope at x.
3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

1) $\frac{1}{{(x + 2)}^{2}}$ $1/(x + 2)^2$
2) $\frac{1}{{(0 + 2)}^{2}} = \frac{1}{4}$ $1/(0 + 2)^2 = 1/4$
3) $f (0) = \frac{0 + 1}{0 + 2} = \frac{1}{2}$ $f(0) = (0 + 1)/(0 + 2) = 1/2$
4) $y - \frac{1}{2} = \frac{1}{4} (x - 0)$ $y - 1/2 = 1/4(x - 0)$

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How do you find the equation of the tangent line to the curve $f (x) = \frac{x + 1}{x + 2}$ $f(x)= (x+1)/(x+2)$ at x=0?

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Explanation:

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How do you find the equation of the tangent line to the curve $f (x) = \frac{x + 1}{x + 2}$ $f(x)= (x+1)/(x+2)$ at x=0?