What is the tangent of x^3-3x^2+3x-3 ?

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

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tangent of x^3-3x^2+3x-3

tangent of

x^{3} - 3 x^{2} + 3 x - 3

y = (3 a_{0}^{2} - 6 a_{0} + 3) x - 2 a_{0}^{3} + 3 a_{0}^{2} - 3

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = x^{3} - 3 x^{2} + 3 x - 3 : \frac{d y}{d x} = 3 x^{2} - 6 x + 3

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} - 6 a_{0} + 3

Find the line with slope m=

3 a_{0}^{2} - 6 a_{0} + 3

and passing through

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

y = (3 a_{0}^{2} - 6 a_{0} + 3) x - 2 a_{0}^{3} + 3 a_{0}^{2} - 3

(7 x^{\frac{1}{5}}) - (6 x^{\frac{4}{7}})

\frac{d}{d x} (5 2 x + 6)

x \to 1 lim (\frac{3}{x + 1})

\int (x^{2} - x)^{4} (2 x - 1) d x

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

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