What is the tangent of 9x+2x^2 ?

The tangent of 9x+2x^2 is y=(9+4a_{0})x-2a_{0}^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of 9x+2x^2

tangent of

9 x + 2 x^{2}

y = (9 + 4 a_{0}) x - 2 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 9 a_{0} + 2 a_{0}^{2})

Find the slope of

y = 9 x + 2 x^{2} : \frac{d y}{d x} = 9 + 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 = 9 + 4 a_{0}

Find the line with slope m=

9 + 4 a_{0}

and passing through

(a_{0}, 9 a_{0} + 2 a_{0}^{2}) : y = (9 + 4 a_{0}) x - 2 a_{0}^{2}

y = (9 + 4 a_{0}) x - 2 a_{0}^{2}

What is the tangent of 9x+2x^2 ?
The tangent of 9x+2x^2 is y=(9+4a_{0})x-2a_{0}^2