What is the tangent of y=5x-x^2 ?

The tangent of y=5x-x^2 is y=(5-2a_{0})x+a_{0}^2

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tangent of y=5x-x^2

tangent of

y = 5 x - x^{2}

y = (5 - 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}, 5 a_{0} - a_{0}^{2})

Find the slope of

y = 5 x - x^{2} : \frac{d y}{d x} = 5 - 2 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 5 - 2 a_{0}

Find the line with slope m=

5 - 2 a_{0}

and passing through

(a_{0}, 5 a_{0} - a_{0}^{2}) : y = (5 - 2 a_{0}) x + a_{0}^{2}

y = (5 - 2 a_{0}) x + a_{0}^{2}

\frac{d}{d x} (2 sec (x) + tan (x))

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

f (x) = ln (cos (3 x))

\frac{\partial}{\partial x} (x^{3} e 3 x y)

\frac{d}{d x} (y^{2} cos (x))

What is the tangent of y=5x-x^2 ?
The tangent of y=5x-x^2 is y=(5-2a_{0})x+a_{0}^2