What is the tangent of 2x^3-2x^2+1 ?

The tangent of 2x^3-2x^2+1 is y=(6a_{0}^2-4a_{0})x-4a_{0}^3+2a_{0}^2+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of 2x^3-2x^2+1

tangent of

2 x^{3} - 2 x^{2} + 1

y = (6 a_{0}^{2} - 4 a_{0}) x - 4 a_{0}^{3} + 2 a_{0}^{2} + 1

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} - 2 a_{0}^{2} + 1)

Find the slope of

y = 2 x^{3} - 2 x^{2} + 1 : \frac{d y}{d x} = 6 x^{2} - 4 x

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 = 6 a_{0}^{2} - 4 a_{0}

Find the line with slope m=

6 a_{0}^{2} - 4 a_{0}

and passing through

(a_{0}, 2 a_{0}^{3} - 2 a_{0}^{2} + 1) : y = (6 a_{0}^{2} - 4 a_{0}) x - 4 a_{0}^{3} + 2 a_{0}^{2} + 1

y = (6 a_{0}^{2} - 4 a_{0}) x - 4 a_{0}^{3} + 2 a_{0}^{2} + 1

What is the tangent of 2x^3-2x^2+1 ?
The tangent of 2x^3-2x^2+1 is y=(6a_{0}^2-4a_{0})x-4a_{0}^3+2a_{0}^2+1