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} ((x - 1) e^{x})

\frac{d}{d x} (\frac{ln ( 4 x )}{x})

\frac{d}{d x} (x e^{1})

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

\frac{t ^{2}}{2}

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