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

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

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tangent of x^2-2x

tangent of

x^{2} - 2 x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = x^{2} - 2 x

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

Find the line with slope m=

2 a_{0} - 2

and passing through

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

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

\frac{\partial}{\partial y} (\frac{7 y}{x})

7 x^{2} - 8 x + 3

\frac{\partial}{\partial x} (x^{2} y^{2})

\frac{d}{d x} (1 - cos (3 x))

x \to - 4 - lim (x + 4)