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

Compute the slope of

y = x - x^{2}

x = a_{0} : 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}

\int 8 x + 6 d x

\frac{\partial}{\partial y} ((y - 5) (x + 5)^{2})

\frac{d}{d x} (x^{4} - 20 x^{2} + 64)

\int 8 cos^{3} (2 θ) sin (2 θ) d θ

x \to 0 lim (\frac{tan ( a x )}{x})