What is the tangent of 6x-x^2 ?

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

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tangent of 6x-x^2

tangent of

6 x - x^{2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 6 x - x^{2}

x = a_{0} : m = 6 - 2 a_{0}

Find the line with slope m=

6 - 2 a_{0}

and passing through

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

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

\frac{( 3 + 3 s )}{s ^{2} + 0.5}

\frac{( cos ( x ) )}{1 - sin ( x )}

\frac{2}{x + 3}

18 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

\frac{\partial}{\partial w} (u v - w)