What is the tangent of f(x)=6x-x^2 ?

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

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tangent of f(x)=6x-x^2

tangent of

f (x) = 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

f (x) = 6 x - x^{2} : \frac{df ( x )}{d x} = 6 - 2 x

Compute the slope of

f (x) = 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}

8 - x^{2}, x^{2}, x = - 3, x = 3

\frac{d}{d x} (\frac{4 x}{3 x ^{2} + 6 x - 8})

\int 17 d x

\frac{\partial}{\partial y} ((x - 1) y^{2} e^{x y})

y^{^{'}} = 5 y + e^{- 2 x} y^{- 2}

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