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

The tangent of y=6+4x^2-2x^3 is y=(-6a_{0}^2+8a_{0})x+4a_{0}^3-4a_{0}^2+6

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tangent of y=6+4x^2-2x^3

tangent of

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

y = (- 6 a_{0}^{2} + 8 a_{0}) x + 4 a_{0}^{3} - 4 a_{0}^{2} + 6

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 6 + 4 x^{2} - 2 x^{3} : \frac{d y}{d x} = - 6 x^{2} + 8 x

Compute the slope of

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

x = a_{0} : m = - 6 a_{0}^{2} + 8 a_{0}

Find the line with slope m=

- 6 a_{0}^{2} + 8 a_{0}

and passing through

(a_{0}, 6 + 4 a_{0}^{2} - 2 a_{0}^{3}) : y = (- 6 a_{0}^{2} + 8 a_{0}) x + 4 a_{0}^{3} - 4 a_{0}^{2} + 6

y = (- 6 a_{0}^{2} + 8 a_{0}) x + 4 a_{0}^{3} - 4 a_{0}^{2} + 6

\int_{1}^{\infty} 2 e^{- x} d x

\frac{d}{d x} ((3 x)^{2 x})

n = 0 \sum \infty \frac{n}{e ^{n^{2}}}

\frac{\partial}{\partial y} (yz e^{x})

\int ln (1 + x^{2}) d x

What is the tangent of y=6+4x^2-2x^3 ?
The tangent of y=6+4x^2-2x^3 is y=(-6a_{0}^2+8a_{0})x+4a_{0}^3-4a_{0}^2+6