What is the tangent of 2x^3+3x^2-12x+6 ?

The tangent of 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 2x^3+3x^2-12x+6

tangent of

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

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

Compute the slope of

y = 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

\int \frac{1}{x 225 x ^{2} - 225} d x

\int \frac{x}{( 7 ^{2} - x ^{2} ) ^{3}} d x

\frac{\partial}{\partial x} (e^{y} - 3)

\frac{d}{d x} ((2 x^{2} - 5)^{- 15})

f (x) = (x - 5)^{2}, at x = 1

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