What is the tangent of 2x^3+36x^2+210x+14 ?

The tangent of 2x^3+36x^2+210x+14 is y=(6a_{0}^2+72a_{0}+210)x-4a_{0}^3-36a_{0}^2+14

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tangent of 2x^3+36x^2+210x+14

tangent of

2 x^{3} + 36 x^{2} + 210 x + 14

y = (6 a_{0}^{2} + 72 a_{0} + 210) x - 4 a_{0}^{3} - 36 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} + 36 a_{0}^{2} + 210 a_{0} + 14)

Find the slope of

y = 2 x^{3} + 36 x^{2} + 210 x + 14 : \frac{d y}{d x} = 6 x^{2} + 72 x + 210

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 = 6 a_{0}^{2} + 72 a_{0} + 210

Find the line with slope m=

6 a_{0}^{2} + 72 a_{0} + 210

and passing through

(a_{0}, 2 a_{0}^{3} + 36 a_{0}^{2} + 210 a_{0} + 14) : y = (6 a_{0}^{2} + 72 a_{0} + 210) x - 4 a_{0}^{3} - 36 a_{0}^{2} + 14

y = (6 a_{0}^{2} + 72 a_{0} + 210) x - 4 a_{0}^{3} - 36 a_{0}^{2} + 14

What is the tangent of 2x^3+36x^2+210x+14 ?
The tangent of 2x^3+36x^2+210x+14 is y=(6a_{0}^2+72a_{0}+210)x-4a_{0}^3-36a_{0}^2+14