What is the tangent of f(x)=(x-3)(x^2-6x+6) ?

The tangent of f(x)=(x-3)(x^2-6x+6) is y=(3a_{0}^2-18a_{0}+24)x-2a_{0}^3+9a_{0}^2-18

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tangent of f(x)=(x-3)(x^2-6x+6)

tangent of

f (x) = (x - 3) (x^{2} - 6 x + 6)

y = (3 a_{0}^{2} - 18 a_{0} + 24) x - 2 a_{0}^{3} + 9 a_{0}^{2} - 18

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (a_{0} - 3) (a_{0}^{2} - 6 a_{0} + 6))

Find the slope of

f (x) = (x - 3) (x^{2} - 6 x + 6) : \frac{df ( x )}{d x} = 3 x^{2} - 18 x + 24

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 3 a_{0}^{2} - 18 a_{0} + 24

Find the line with slope m=

3 a_{0}^{2} - 18 a_{0} + 24

and passing through

(a_{0}, (a_{0} - 3) (a_{0}^{2} - 6 a_{0} + 6)) : y = (3 a_{0}^{2} - 18 a_{0} + 24) x - 2 a_{0}^{3} + 9 a_{0}^{2} - 18

y = (3 a_{0}^{2} - 18 a_{0} + 24) x - 2 a_{0}^{3} + 9 a_{0}^{2} - 18

e^{- s} \frac{1}{s}

4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

\int_{0}^{100} e^{- \frac{x}{0.033}} d x

f (x) = (x^{3} - 2)^{3}

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

What is the tangent of f(x)=(x-3)(x^2-6x+6) ?
The tangent of f(x)=(x-3)(x^2-6x+6) is y=(3a_{0}^2-18a_{0}+24)x-2a_{0}^3+9a_{0}^2-18