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

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

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tangent of (x-2)(x^2+4)

tangent of

(x - 2) (x^{2} + 4)

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

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

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

Find the line with slope m=

3 a_{0}^{2} - 4 a_{0} + 4

and passing through

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

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

6 cos (x)

- \frac{2}{9 ( 1 + x ) ^{\frac{5}{3}}}

\frac{d}{d x} (tan (\frac{π x}{2}))

y = 3 + \frac{12}{2 - x}

10 x (x^{2} + 7)^{4}

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