What is the tangent of 2x^3+3x^2-12x+4 ?

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

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tangent of 2x^3+3x^2-12x+4

tangent of

2 x^{3} + 3 x^{2} - 12 x + 4

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

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} + 4)

Find the slope of

y = 2 x^{3} + 3 x^{2} - 12 x + 4 : \frac{d y}{d x} = 6 x^{2} + 6 x - 12

Compute the slope of

y = 2 x^{3} + 3 x^{2} - 12 x + 4

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

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

\frac{\partial}{\partial x} (x^{2} \cdot y + \frac{x e ^{x}}{y ^{3}})

\int \frac{1}{3 + 2 x ^{2}} d x

\int (2) d x

\int (tan (x) + cot (x)) d x

x \to 0 + lim ((\frac{1}{x})^{x^{2}})

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