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

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

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tangent of f(x)=12x-x^3

tangent of

f (x) = 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

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

Compute the slope of

f (x) = 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}

\int - cos (n x) d x

\frac{d y}{d x} = \frac{x ^{3} + y ^{3}}{x y ^{2}}

\int_{0}^{\frac{1}{2}} 8 x - \frac{1}{2} x d x

x \to - 2 lim (x^{5} + 4 x^{3} - 5 x - 2)

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