What is the tangent of f(x)=x^3+2x^2+4 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tangent of f(x)=x^3+2x^2+4

tangent of

f (x) = x^{3} + 2 x^{2} + 4

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{3} + 2 a_{0}^{2} + 4)

Find the slope of

f (x) = x^{3} + 2 x^{2} + 4 : \frac{df ( x )}{d x} = 3 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 = 3 a_{0}^{2} + 4 a_{0}

Find the line with slope m=

3 a_{0}^{2} + 4 a_{0}

and passing through

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

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

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