What is the tangent of y=2x^3+3x^2-12x+3 ?

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

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tangent of y=2x^3+3x^2-12x+3

tangent of

y = 2 x^{3} + 3 x^{2} - 12 x + 3

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} + 3 a_{0}^{2} - 12 a_{0} + 3)

Find the slope of

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

Compute the slope of

y = 2 x^{3} + 3 x^{2} - 12 x + 3

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

Find the line with slope m=

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

and passing through

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

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

\frac{d}{d x} ((2 - x)^{4})

(u - u) (u + u)

y^{^{'}} + 2 y = e^{- x}

\int 2 x \cdot cos (x^{2}) d x

x y^{^{'}} = 2 x + 3 y

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