What is the tangent of 12x-x^3 ?

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

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tangent of 12x-x^3

tangent of

12 x - x^{3}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 12 x - x^{3}

x = a_{0} : m = 12 - 3 a_{0}^{2}

Find the line with slope m=

12 - 3 a_{0}^{2}

and passing through

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

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

x \to - 2 lim (3^{x + 1})

\int w^{2} ln (w) d w

2 x + 4

\frac{1}{2 t ^{2} + 1}

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

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