What is the tangent of f(x)=4(x-1/x)^3,\at x=2 ?

The tangent of f(x)=4(x-1/x)^3,\at x=2 is y= 135/4 x-54

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of f(x)=4(x-1/x)^3,\at x=2

tangent of

f (x) = 4 (x - \frac{1}{x})^{3}, at x = 2

y = \frac{135}{4} x - 54

Solution steps

Find the tangent point:

(2, \frac{27}{2})

Find the slope of

f (x) = 4 (x - \frac{1}{x})^{3} : \frac{df ( x )}{d x} = 12 x^{2} + \frac{12}{x ^{4}} - \frac{12}{x ^{2}} - 12

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{135}{4}

Find the line with slope m=

\frac{135}{4}

and passing through

(2, \frac{27}{2}) : y = \frac{135}{4} x - 54

y = \frac{135}{4} x - 54

What is the tangent of f(x)=4(x-1/x)^3,\at x=2 ?
The tangent of f(x)=4(x-1/x)^3,\at x=2 is y= 135/4 x-54