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

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

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tangent of y=6x-x^2

tangent of

y = 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{d}{d x} ((2 e^{x} + x^{2}) ln (x))

x \to 1 lim (x)

\frac{1}{s ^{2}} - \frac{1}{s} + \frac{1}{( s - 2 )}

\int \frac{x ^{2} + 2 x}{x ^{2} + 2 x + 1} d x

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

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