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

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

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

tangent of

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

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

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

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

Find the line with slope m=

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

and passing through

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

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

\frac{\partial}{\partial x} (e^{c o s (x - 2 y)})

\frac{( 7 s + 2 )}{s ^{2} + 6 s + 34}

x \to 9 + lim (\frac{7}{x - 9})

\int e^{y} cos (x) d x

\frac{sin ( 2 x )}{2}

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