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

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

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

tangent of

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

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

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} + 2 a_{0} - 2)

Find the slope of

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

Compute the slope of

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

x = a_{0} : m = 3 a_{0}^{2} - 6 a_{0} + 2

Find the line with slope m=

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

and passing through

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

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

\frac{d}{d x} (I n x)

f (x) = x^{3} - 2 x^{2} + 1, at x = 1

\frac{d}{d x} (arcsin (e^{2 x}))

\int \frac{x ^{4}}{5} d x

\frac{d}{d x} (4 x^{2} \cdot sin (4 x))

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