What is the tangent of 2x^3+36x^2+210x+11 ?

The tangent of 2x^3+36x^2+210x+11 is y=(6a_{0}^2+72a_{0}+210)x-4a_{0}^3-36a_{0}^2+11

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tangent of 2x^3+36x^2+210x+11

tangent of

2 x^{3} + 36 x^{2} + 210 x + 11

y = (6 a_{0}^{2} + 72 a_{0} + 210) x - 4 a_{0}^{3} - 36 a_{0}^{2} + 11

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} + 11)

Find the slope of

y = 2 x^{3} + 36 x^{2} + 210 x + 11 : \frac{d y}{d x} = 6 x^{2} + 72 x + 210

Compute the slope of

y = 2 x^{3} + 36 x^{2} + 210 x + 11

x = a_{0} : 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} + 11) : y = (6 a_{0}^{2} + 72 a_{0} + 210) x - 4 a_{0}^{3} - 36 a_{0}^{2} + 11

y = (6 a_{0}^{2} + 72 a_{0} + 210) x - 4 a_{0}^{3} - 36 a_{0}^{2} + 11

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What is the tangent of 2x^3+36x^2+210x+11 ?
The tangent of 2x^3+36x^2+210x+11 is y=(6a_{0}^2+72a_{0}+210)x-4a_{0}^3-36a_{0}^2+11