What is the tangent of 2x^3-6x^2-90x+1 ?

The tangent of 2x^3-6x^2-90x+1 is y=(6a_{0}^2-12a_{0}-90)x-4a_{0}^3+6a_{0}^2+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of 2x^3-6x^2-90x+1

tangent of

2 x^{3} - 6 x^{2} - 90 x + 1

y = (6 a_{0}^{2} - 12 a_{0} - 90) x - 4 a_{0}^{3} + 6 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} - 6 a_{0}^{2} - 90 a_{0} + 1)

Find the slope of

y = 2 x^{3} - 6 x^{2} - 90 x + 1 : \frac{d y}{d x} = 6 x^{2} - 12 x - 90

Compute the slope of

y = 2 x^{3} - 6 x^{2} - 90 x + 1

x = a_{0} : m = 6 a_{0}^{2} - 12 a_{0} - 90

Find the line with slope m=

6 a_{0}^{2} - 12 a_{0} - 90

and passing through

(a_{0}, 2 a_{0}^{3} - 6 a_{0}^{2} - 90 a_{0} + 1) : y = (6 a_{0}^{2} - 12 a_{0} - 90) x - 4 a_{0}^{3} + 6 a_{0}^{2} + 1

y = (6 a_{0}^{2} - 12 a_{0} - 90) x - 4 a_{0}^{3} + 6 a_{0}^{2} + 1

4 x - 4 x

f (x) = e^{8 x}

x \to \frac{x}{4} lim (tan (2 x))

\int cos (2 x) e^{3 x} d x

y = arctan (x)

What is the tangent of 2x^3-6x^2-90x+1 ?
The tangent of 2x^3-6x^2-90x+1 is y=(6a_{0}^2-12a_{0}-90)x-4a_{0}^3+6a_{0}^2+1