What is the tangent of x-x^3(1) ?

The tangent of x-x^3(1) is y=(1-3a_{0}^2)x+2a_{0}^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of x-x^3(1)

tangent of

x - x^{3} (1)

y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} - a_{0}^{3})

Find the slope of

y = x - x^{3} 1 : \frac{d y}{d x} = 1 - 3 x^{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 = 1 - 3 a_{0}^{2}

Find the line with slope m=

1 - 3 a_{0}^{2}

and passing through

(a_{0}, a_{0} - a_{0}^{3}) : y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

y = (1 - 3 a_{0}^{2}) x + 2 a_{0}^{3}

What is the tangent of x-x^3(1) ?
The tangent of x-x^3(1) is y=(1-3a_{0}^2)x+2a_{0}^3