What is the tangent of f(x)=2x^3+3x^2-12x+6 ?

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

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tangent of f(x)=2x^3+3x^2-12x+6

tangent of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6

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

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} + 6)

Find the slope of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6 : \frac{df ( x )}{d x} = 6 x^{2} + 6 x - 12

Compute the slope of

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6

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

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

ln (1 + x^{3})

\int - 5 csc^{2} (x) + 5 d x

\int (x e^{- x}) d x

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

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