What is the tangent of f(x)= 2/(x+3),\at a=-4 ?

The tangent of f(x)= 2/(x+3),\at a=-4 is y=-2/((a+3)^2)x+(4a+6)/((a+3)^2)

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tangent of f(x)= 2/(x+3),\at a=-4

tangent of

f (x) = \frac{2}{x + 3}, at a = - 4

y = - \frac{2}{( a + 3 ) ^{2}} x + \frac{4 a + 6}{( a + 3 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, \frac{2}{a + 3})

Find the slope of

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

Compute the slope of

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

x = a : m = - \frac{2}{( a + 3 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a + 3 ) ^{2}}

and passing through

(a, \frac{2}{a + 3}) : y = - \frac{2}{( a + 3 ) ^{2}} x + \frac{4 a + 6}{( a + 3 ) ^{2}}

y = - \frac{2}{( a + 3 ) ^{2}} x + \frac{4 a + 6}{( a + 3 ) ^{2}}

n = 1 \sum \infty sin (n + 1)

(10 - x) y^{2} = x^{3}, (2, 1)

\int \frac{1}{16 x ^{2} + 4} d x

x + (x - 6)^{6}

\int x (x - 1) d x

What is the tangent of f(x)= 2/(x+3),\at a=-4 ?
The tangent of f(x)= 2/(x+3),\at a=-4 is y=-2/((a+3)^2)x+(4a+6)/((a+3)^2)