What is the tangent of 2x^3-4x+6 ?

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

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tangent of 2x^3-4x+6

tangent of

2 x^{3} - 4 x + 6

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} - 4 a_{0} + 6)

Find the slope of

y = 2 x^{3} - 4 x + 6 : \frac{d y}{d x} = 6 x^{2} - 4

Compute the slope of

y = 2 x^{3} - 4 x + 6

x = a_{0} : m = 6 a_{0}^{2} - 4

Find the line with slope m=

6 a_{0}^{2} - 4

and passing through

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

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

\frac{\partial}{\partial x} (5 - 3 x + 6 y - 2 x^{2} y)

(1, 6), (7, 3)

\int x^{3} y d y

\frac{d y}{d x} = 3 y x^{2} - 3 x^{2}

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{9}})

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