What is the tangent of x-x^2 ?

The tangent of x-x^2 is y=(1-2a_{0})x+a_{0}^2

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tangent of x-x^2

tangent of

x - x^{2}

y = (1 - 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}, a_{0} - a_{0}^{2})

Find the slope of

y = x - x^{2} : \frac{d y}{d x} = 1 - 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 = 1 - 2 a_{0}

Find the line with slope m=

1 - 2 a_{0}

and passing through

(a_{0}, a_{0} - a_{0}^{2}) : y = (1 - 2 a_{0}) x + a_{0}^{2}

y = (1 - 2 a_{0}) x + a_{0}^{2}