What is the tangent of f(x)= 3/(x+2),\at x=3 ?

The tangent of f(x)= 3/(x+2),\at x=3 is y=-3/25 x+24/25

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tangent of f(x)= 3/(x+2),\at x=3

tangent of

f (x) = \frac{3}{x + 2}, at x = 3

y = - \frac{3}{25} x + \frac{24}{25}

Solution steps

Find the tangent point:

(3, \frac{3}{5})

Find the slope of

f (x) = \frac{3}{x + 2} : \frac{df ( x )}{d x} = - \frac{3}{( x + 2 ) ^{2}}

Compute the slope of

f (x) = \frac{3}{x + 2}

x = 3 : m = - \frac{3}{25}

Find the line with slope m=

- \frac{3}{25}

and passing through

(3, \frac{3}{5}) : y = - \frac{3}{25} x + \frac{24}{25}

y = - \frac{3}{25} x + \frac{24}{25}

sin (9 x) + cos (2 x)

\int \frac{1 - z}{- 1 - z}

(ln (x))^{^{'}}

\int (x^{2} - 2 x - 3) d x

(x^{2} + 1) y^{^{'}} + y^{2} + 1 = 0, y (4) = e

What is the tangent of f(x)= 3/(x+2),\at x=3 ?
The tangent of f(x)= 3/(x+2),\at x=3 is y=-3/25 x+24/25