What is the tangent of 4x(x^2-4) ?

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

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tangent of 4x(x^2-4)

tangent of

4 x (x^{2} - 4)

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0} (a_{0}^{2} - 4))

Find the slope of

y = 4 x (x^{2} - 4) : \frac{d y}{d x} = 4 (3 x^{2} - 4)

Compute the slope of

y = 4 x (x^{2} - 4)

x = a_{0} : m = 4 (3 a_{0}^{2} - 4)

Find the line with slope m=

4 (3 a_{0}^{2} - 4)

and passing through

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

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

g (x) = x^{4} - \frac{6}{x}, (2, 13)

4 cot^{7} (x), at x = \frac{π}{4}

\frac{\partial}{\partial y} (2 y^{2} x)

x \to 8 lim (\frac{3 x ^{2} - 24 x}{x ^{2} - 64})

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

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