What is the tangent of 7x-x^2 ?

The tangent of 7x-x^2 is y=(7-2a_{0})x+a_{0}^2

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tangent of 7x-x^2

tangent of

7 x - x^{2}

y = (7 - 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}, 7 a_{0} - a_{0}^{2})

Find the slope of

y = 7 x - x^{2} : \frac{d y}{d x} = 7 - 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 = 7 - 2 a_{0}

Find the line with slope m=

7 - 2 a_{0}

and passing through

(a_{0}, 7 a_{0} - a_{0}^{2}) : y = (7 - 2 a_{0}) x + a_{0}^{2}

y = (7 - 2 a_{0}) x + a_{0}^{2}

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