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

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

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

tangent of

f (x) = x^{3} - 12 x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

f (x) = x^{3} - 12 x

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

Find the line with slope m=

3 a_{0}^{2} - 12

and passing through

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

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

\int (\frac{3}{5}) cos (x) d x

\frac{d}{d x} (\frac{2 x + 1}{x + 2})

\frac{d}{d x} (ln (\frac{7 + e ^{x}}{7 - e ^{x}}))

\int_{0}^{5} \frac{1}{x ^{\frac{13}{12}}} d x

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