What is the tangent of f(x)=(x+1)(6x^2-6x-12) ?

The tangent of f(x)=(x+1)(6x^2-6x-12) is y=(18a_{0}^2-18)x-12a_{0}^3-12

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tangent of f(x)=(x+1)(6x^2-6x-12)

tangent of

f (x) = (x + 1) (6 x^{2} - 6 x - 12)

y = (18 a_{0}^{2} - 18) x - 12 a_{0}^{3} - 12

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (a_{0} + 1) (6 a_{0}^{2} - 6 a_{0} - 12))

Find the slope of

f (x) = (x + 1) (6 x^{2} - 6 x - 12) : \frac{df ( x )}{d x} = 18 x^{2} - 18

Compute the slope of

f (x) = (x + 1) (6 x^{2} - 6 x - 12)

x = a_{0} : m = 18 a_{0}^{2} - 18

Find the line with slope m=

18 a_{0}^{2} - 18

and passing through

(a_{0}, (a_{0} + 1) (6 a_{0}^{2} - 6 a_{0} - 12)) : y = (18 a_{0}^{2} - 18) x - 12 a_{0}^{3} - 12

y = (18 a_{0}^{2} - 18) x - 12 a_{0}^{3} - 12

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What is the tangent of f(x)=(x+1)(6x^2-6x-12) ?
The tangent of f(x)=(x+1)(6x^2-6x-12) is y=(18a_{0}^2-18)x-12a_{0}^3-12