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

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

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

tangent of

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

y = 3 x + 4

Solution steps

Find the tangent point:

(- 2, - 2)

Find the slope of

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

Compute the slope of

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

x = - 2 : m = 3

Find the line with slope m=

3

and passing through

(- 2, - 2) : y = 3 x + 4

y = 3 x + 4

t \to + 0 lim (\frac{sin ( 2 t )}{t})

\frac{( s + 2 )}{( s ^{2} + 4 s + 13 )}

t^{2} \frac{d x}{d t} + 3 t x = t^{4} lo g_{10} (t) + 1

\frac{1}{x + x ln ( x )}

f (x) = (4 x^{2} + 3) (4 x - 5)

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