What is the tangent of f(x)=2x^3+42x^2+288x+14 ?

The tangent of f(x)=2x^3+42x^2+288x+14 is y=(6a_{0}^2+84a_{0}+288)x-4a_{0}^3-42a_{0}^2+14

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of f(x)=2x^3+42x^2+288x+14

tangent of

f (x) = 2 x^{3} + 42 x^{2} + 288 x + 14

y = (6 a_{0}^{2} + 84 a_{0} + 288) x - 4 a_{0}^{3} - 42 a_{0}^{2} + 14

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} + 42 a_{0}^{2} + 288 a_{0} + 14)

Find the slope of

f (x) = 2 x^{3} + 42 x^{2} + 288 x + 14 : \frac{df ( x )}{d x} = 6 x^{2} + 84 x + 288

Compute the slope of

f (x) = 2 x^{3} + 42 x^{2} + 288 x + 14

x = a_{0} : m = 6 a_{0}^{2} + 84 a_{0} + 288

Find the line with slope m=

6 a_{0}^{2} + 84 a_{0} + 288

and passing through

(a_{0}, 2 a_{0}^{3} + 42 a_{0}^{2} + 288 a_{0} + 14) : y = (6 a_{0}^{2} + 84 a_{0} + 288) x - 4 a_{0}^{3} - 42 a_{0}^{2} + 14

y = (6 a_{0}^{2} + 84 a_{0} + 288) x - 4 a_{0}^{3} - 42 a_{0}^{2} + 14

y = 2 - 6 x

\int (3 + x)^{2} d x

f (x) = - x^{2}

x \to 7 lim (\frac{3}{x - 7})

x \to 0 lim (\frac{3 x}{x ^{2} + 2 x})

What is the tangent of f(x)=2x^3+42x^2+288x+14 ?
The tangent of f(x)=2x^3+42x^2+288x+14 is y=(6a_{0}^2+84a_{0}+288)x-4a_{0}^3-42a_{0}^2+14