What is the tangent of f(x)=(3x)/(x+1),\at x=2 ?

The tangent of f(x)=(3x)/(x+1),\at x=2 is y= 1/3 x+4/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of f(x)=(3x)/(x+1),\at x=2

tangent of

f (x) = \frac{3 x}{x + 1}, at x = 2

y = \frac{1}{3} x + \frac{4}{3}

Solution steps

Find the tangent point:

(2, 2)

Find the slope of

f (x) = \frac{3 x}{x + 1} : \frac{df ( x )}{d x} = \frac{3}{( x + 1 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{3}

Find the line with slope m=

\frac{1}{3}

and passing through

(2, 2) : y = \frac{1}{3} x + \frac{4}{3}

y = \frac{1}{3} x + \frac{4}{3}

What is the tangent of f(x)=(3x)/(x+1),\at x=2 ?
The tangent of f(x)=(3x)/(x+1),\at x=2 is y= 1/3 x+4/3