What is the tangent of x^4-20x^2+64 ?

The tangent of x^4-20x^2+64 is y=(4a_{0}^3-40a_{0})x-3a_{0}^4+20a_{0}^2+64

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of x^4-20x^2+64

tangent of

x^{4} - 20 x^{2} + 64

y = (4 a_{0}^{3} - 40 a_{0}) x - 3 a_{0}^{4} + 20 a_{0}^{2} + 64

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 20 a_{0}^{2} + 64)

Find the slope of

y = x^{4} - 20 x^{2} + 64 : \frac{d y}{d x} = 4 x^{3} - 40 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 = 4 a_{0}^{3} - 40 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 40 a_{0}

and passing through

(a_{0}, a_{0}^{4} - 20 a_{0}^{2} + 64) : y = (4 a_{0}^{3} - 40 a_{0}) x - 3 a_{0}^{4} + 20 a_{0}^{2} + 64

y = (4 a_{0}^{3} - 40 a_{0}) x - 3 a_{0}^{4} + 20 a_{0}^{2} + 64

What is the tangent of x^4-20x^2+64 ?
The tangent of x^4-20x^2+64 is y=(4a_{0}^3-40a_{0})x-3a_{0}^4+20a_{0}^2+64