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

The tangent of y=2x-2x^2 is y=(2-4a_{0})x+2a_{0}^2

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tangent of y=2x-2x^2

tangent of

y = 2 x - 2 x^{2}

y = (2 - 4 a_{0}) x + 2 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0} - 2 a_{0}^{2})

Find the slope of

y = 2 x - 2 x^{2} : \frac{d y}{d x} = 2 - 4 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 = 2 - 4 a_{0}

Find the line with slope m=

2 - 4 a_{0}

and passing through

(a_{0}, 2 a_{0} - 2 a_{0}^{2}) : y = (2 - 4 a_{0}) x + 2 a_{0}^{2}

y = (2 - 4 a_{0}) x + 2 a_{0}^{2}

x \to 2 lim (\frac{1}{2} x^{2} - 4 x)

2 e^{2 t}

x = - 2, x = 3, y = 2 x^{2} + 2, y = 0

2 x^{2} + x - 1, at x = - 1

\int cot^{5} (x) sin^{4} (x) d x

What is the tangent of y=2x-2x^2 ?
The tangent of y=2x-2x^2 is y=(2-4a_{0})x+2a_{0}^2