What is the tangent of 2x^3-6x^2-18-3 ?

The tangent of 2x^3-6x^2-18-3 is y=(6a_{0}^2-12a_{0})x-4a_{0}^3+6a_{0}^2-21

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tangent of 2x^3-6x^2-18-3

tangent of

2 x^{3} - 6 x^{2} - 18 - 3

y = (6 a_{0}^{2} - 12 a_{0}) x - 4 a_{0}^{3} + 6 a_{0}^{2} - 21

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} - 6 a_{0}^{2} - 21)

Find the slope of

y = 2 x^{3} - 6 x^{2} - 18 - 3 : \frac{d y}{d x} = 6 x^{2} - 12 x

Compute the slope of

y = 2 x^{3} - 6 x^{2} - 18 - 3

x = a_{0} : m = 6 a_{0}^{2} - 12 a_{0}

Find the line with slope m=

6 a_{0}^{2} - 12 a_{0}

and passing through

(a_{0}, 2 a_{0}^{3} - 6 a_{0}^{2} - 21) : y = (6 a_{0}^{2} - 12 a_{0}) x - 4 a_{0}^{3} + 6 a_{0}^{2} - 21

y = (6 a_{0}^{2} - 12 a_{0}) x - 4 a_{0}^{3} + 6 a_{0}^{2} - 21

y = - 2 x^{2} + 6, y = - 2

\int 1 + x^{2} \cdot x^{5} d x

y = - x^{3} + 2 x^{2} - 4, at x = - 1

- sec^{2} (x)

What is the tangent of 2x^3-6x^2-18-3 ?
The tangent of 2x^3-6x^2-18-3 is y=(6a_{0}^2-12a_{0})x-4a_{0}^3+6a_{0}^2-21